, An ABC of Lying, 2004.

F. D'agostini, B. Menzogna, and . Boringhieri, Spanish translation: Mentira, 2012.

P. Eldridge-smith, The Cretan Liar Paradox, An ABC of Lying, pp.71-92, 2004.

P. Eldridge-smith, Pinocchio against the dialetheists, Analysis, vol.71, issue.2, pp.306-308, 2011.

P. Eldridge-smith, Pinocchio beards the Barber, vol.72, pp.749-752, 2012.

V. Eldridge-smith and &. P. Eldridge-smith, The Pinocchio paradox, Analysis, vol.70, pp.212-215, 2010.

H. Field, Saving Truth from Paradox, 2008.

I. Kant, Theorie-Werkausgabe, Werke in zwölf Bänden, Bd. VIII, 1968.

J. Lackey, Learning From Words. Testimony as a Source of Knowledge, 2008.

J. Lackey, Lies and deception: an unhappy divorce, Analysis, vol.73, issue.2, 2013.

J. E. Mahon, The Definition of Lying and Deception, The Stanford Encyclopedia of Philosophy, 2016.

N. Marsili, Lying as a Scalar Phenomenon: Insincerity along the Certainty-Uncertainty Continuum, Certainty-uncertainty -and the Attitudinal Space in Between, 2014.

G. Orwell, , 1949.

J. Saul, Did Clinton say something false?, Analysis, vol.60, pp.255-257, 2000.

. Tutorials,

J. Saul, Lying, Misleading, and What is Said, 2012.

J. Saul, Just go ahead and lie, Analysis, vol.72, issue.1, 2012.

R. A. Sorensen, Permission to Cheat, Analysis, vol.67, pp.205-214, 2007.
DOI : 10.1111/j.1467-8284.2007.00675.x

R. A. Sorensen, Bald-faced Lies! Lying without the intent to deceive, Pacific Philosophical Quarterly, vol.88, issue.2, pp.251-264, 2007.

R. A. Sorensen, Knowledge-Lies, Analysis, vol.70, issue.4, pp.608-615, 2010.
DOI : 10.1093/analys/anq072

J. Webber, Liar!, Analysis, vol.73, issue.4, 2013.

B. Williams, Truth and Truthfulness. An Essay in Genealogy, 2002.

O. Caramello, Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges, 2017.

O. Caramello, Grothendieck toposes as unifying 'bridges' in Mathematics, 2016.

S. Maclane and &. Moerdijk, Sheaves in Geometry and Logic, 1994.

M. Makkai and &. G. Reyes, First-Order Categorical Logic, Lecture Notes in Mathematics, vol.611, 1977.

ˆ. Beziau, Rules, derived rules, permissible rules and the various types of systems of deduction, Proof, Types and Categories, pp.159-184, 1999.

ˆ. Beziau, From Consequence Operator to Universal Logic: A Survey of General Abstract Logic, Logica Universalis: Towards a General Theory of Logic, pp.3-17, 2005.

ˆ. Beziau, La Puissance du Symbole, La Pointure du Symbole, pp.9-34, 2014.

ˆ. C. Ducasse and H. B. Curry, Early History of the Association for Symbolic Logic, The Journal of Symbolic Logic, vol.27, issue.3, pp.255-258, 1962.

ˆ. V. Dudman, Frege's Judgement-Stroke, The Philosophical Quarterly, vol.20, pp.150-161, 1970.

ˆ. D. Greimann, The Judgement-Stroke as a Truth-Operator: A New Interpretation of the Logical Form of Sentences in Frege's Scientific Language, Erkenntnis, vol.52, issue.2, pp.213-238, 2000.

ˆ. S. Le´sniewskile´sniewski, On some questions regarding the sense of the logistic theses, Staniss law Le´sniewskiLe´sniewski: Collected Works, vol.2, pp.181-196, 1992.

ˆ. F. Rombout and F. , Russell and Wittgenstein on the Judgment Stroke, 2011.

ˆ. N. Smith, Frege's Judgement Stroke, Australasian Journal of Philosophy, vol.78, issue.2, pp.153-175, 2000.

ˆ. N. Smith, Frege's Judgement Stroke and the Conception of Logic as the Study of Inference not Consequence, Philosophy Compass, vol.4, issue.4, pp.639-665, 2009.

D. Boethius and . Differentiis-topicis, , 1978.

J. Buridan and . Summulae-de-dialectica, , 2001.

J. Buridan, Treatise on Consequences, 2014.
DOI : 10.5422/fordham/9780823257188.001.0001

, The Cambridge Companion to Medieval Logic, 2016.

S. Ebbesen, Greek-Latin Philosophical Interaction, Routledge, 2008.
DOI : 10.4324/9781315253800

N. J. Green-pedersen, The Tradition of the Topics in the Middle Ages, Philosophia, Munich and Vienna, 1984.

R. Kilwardby, Notule Libri Priorum, 2015.

G. Klima and J. Buridan, , 2009.

O. William-of, Ockham's Theory of Terms: Part I of the Summa Logicae, 1974.

P. V. Spade, Five Texts on the Mediaeval Problem of Universals: Porphyry, 1994.

A. Citkin, On an effective problem concerning mutual adequacy of two finite truth-tables, Proceedings of the Fourth Conference on the Occasion of the 30th Anniversary of the Liberation of Carpathians, 1975.

A. Citkin and &. Muravitsky, Lindenbaum method (propositional language), 2016.

J. Czelakowski, Model-Theoretic Methods in Methodology of Propositional Calculi, Institute of Philosophy and Sociology, The Polish Academy of Sciences, 1980.

J. Font, Abstract Algebraic Logic, 2016.

J. Kalicki, A test for the equality of truth-tables, The Journal of Symbolic Logic, vol.17, issue.3, pp.161-163, 1952.

J. Lo's-&-r and . Suszko, Koninklijke Nederlandse Akademie van Wetenschappen, also in Indagationes mathematicae, vol.61, pp.177-183, 1958.

J. C. Mckinsey and &. Tarski, Some theorems about the sentential calculi of Lewis and Heyting, The Journal of Symbolic Logic, vol.13, issue.1, pp.1-15, 1948.

A. Muravitsky, Beyond Rasiowan Systems: Unital Deductive Systems, Logica Universalis, vol.8, issue.1, pp.83-102, 2014.
DOI : 10.1007/s11787-014-0096-2

W. Pogorzelski and &. Wojtylak, Completeness Theory for Propositional Logics, 2000.

H. Rasiowa, An Algebraic Approach to Non-Classical Logics, 1974.

A. Tarski, Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 1956.

R. Wójcicki, Theory of Logical Calculi: Basic Theory of Consequence Operations, 1988.

A. Wrónski, On cardinalities of matrices strongly adequate for the intuitionistic propositional logic, Bulletin of the Section of Logic, vol.3, issue.1, pp.67-72, 1974.

T. W. Adorno, Negative Dialektik, 1966.

T. W. Adorno, Einführung in die Dialektik, 2010.

L. , Logica e dialettica in Hegel, La formalizzazione della dialettica, pp.85-113, 1979.

, The Complete Works of Aristotle, 1984.

E. Berti, Contraddizione e dialettica negli antichi e nei moderni, Morcelliana, 1987.

F. Berto, Che cosá e la dialettica Hegeliana? Un'interpretazione analitica del metodo, Il Poligrafo, 2005.
URL : https://hal.archives-ouvertes.fr/halshs-00790981

B. Croce, Saggio sullo Hegel. Seguito da altri scritti di storia della filosofia, 2006.

F. , Hegel's Interpretation of Megarian Paradoxes. Between Logic and Metaphilosophy, Die Begründung der Philosophie im Deutschen Idealismus, pp.121-140, 2011.

E. Ficara, Dialectic and Dialetheism, History and Philosophy of Logic, vol.34, pp.35-52, 2013.

, Plato: The Collected Dialogues, 1961.

G. W. Hegel, Lectures on the History of Philosophy, p.1896

G. W. Hegel, , 1969.

G. W. Hegel, The Encyclopaedia Logic. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 1991.

J. Hintikka, On Common Factors of Dialectics, Konzepte der Dialektik, pp.109-110, 1981.

W. Kneale and &. Kneale, The Development of Logic, 2008.

, La formalizzazione della dialettica. Hegel, Marx e la logica contemporanea, 1979.

G. Priest, Dialectic and Dialetheic, Science and Society, vol.53, issue.4, pp.388-415, 1989.

G. Priest-&-r.-routley and O. Paraconsistency, Department of Philosophy, Research School of Social Sciences, 1984.

R. Rescher, . Dialectics, . Ontos, and G. Heusenstamm, , 2008.

R. Carnap, Logische Syntax der Sprache, 1934.

C. Chihara, The semantic paradoxes: A diagnostic investigation, Philosophical Review, vol.88, issue.4, pp.590-618, 1979.

C. Chihara, Constructibility and Mathematical Existence, 1990.

C. Chihara, A Structural Account of Mathematics, 2004.

M. Eklund, Inconsistent languages, Philosophy and Phenomenological Research, vol.64, issue.2, pp.251-275, 2002.

H. Field, Science Without Numbers, 1980.

S. Kripke, Outline of a theory of truth, The Journal of Philosophy, vol.72, issue.19, pp.690-716, 1975.

D. Lewis, Conventions, 1969.

T. Nagel, The View from Nowhere, 1986.

K. Scharp, Replacing Truth, 2013.
DOI : 10.1080/00201740701698589

B. Van-fraassen, Singular terms, truth-value gaps, and free logic, The Journal of Philosophy, vol.63, issue.17, pp.481-495, 1966.

G. Brun, Explication as a Method of Conceptual Re-engineering, Erkenntnis, vol.81, issue.6, pp.1211-1241, 2016.

G. Brun, Conceptual re-engineering: from explication to reflective equilibrium, pp.1-30, 2017.

, Conceptual Engineering and Conceptual Ethics

A. Burgess and &. Plunkett, Conceptual ethics I/II, Philosophy Compass, vol.8, issue.12, pp.1102-1110, 2013.
DOI : 10.1111/phc3.12085

H. Cappelen, Fixing Language: Conceptual Engineering and the Limits of Revision

H. Cappelen and Ø. , ConceptLab Research Project (website)

R. Carnap, Logical Foundations of Probability, 1950.

R. Carnap, Replies and systematic expositions, The Philosophy of Rudolf Carnap, pp.859-1113, 1963.

L. Floridi, The method of levels of abstraction, Minds and Machines, vol.18, pp.303-329, 2008.

L. Floridi, A defence of constructionism: Philosophy as conceptual engineering, Metaphilosophy, vol.42, issue.3, pp.282-304, 2011.

L. Floridi, A plea for non-naturalism as constructionism, Minds and Machines, vol.27, pp.269-285, 2017.
DOI : 10.1007/s11023-017-9422-9

URL : https://link.springer.com/content/pdf/10.1007%2Fs11023-017-9422-9.pdf

P. Greenough, Against Conceptual Engineering, Book manuscript

B. Löwe and &. Müller, Data and phenomena in conceptual modelling, Synthese, vol.182, issue.1, pp.131-148, 2011.

E. Machery, Doing without Concepts, 2009.
DOI : 10.1093/acprof:oso/9780195306880.001.0001

R. Menary, Cognitive Integration: Mind and Cognition Unbounded, Palgrave Macmillan, 2007.

G. Piccinini and &. S. Scott, Splitting concepts, Philosophy of Science, vol.73, issue.4, pp.390-409, 2006.
DOI : 10.1086/516806

D. Plunkett, Which concepts should we use? Metalinguistic negotiations and the methodology of philosophy, Inquiry, vol.58, issue.7-8, pp.828-874, 2015.

S. Le´sniewskile´sniewski, Collected Works, vol.2, 1992.

E. C. Luschei, The Logical Systems of Le´sniewskiLe´sniewski, 1962.

D. Miéville, Un développement des systèmes logiques de Staniss law Le-´ sniewski, 1984.

S. Richard, Le´sniewskiLe´sniewski on Metalanguage and Definitions

B. Russell, The Propositional Calculus, chap. II, A of Principles of Mathematics, 1903.

P. Simons, Parts: A Study in Ontology, 1987.

P. Simons, Stanis law Le´sniewskiLe´sniewski, Stanford Encyclopedia of Philosophy, 2015.

B. Soboci´nskisoboci´nski, L'analyse de l'antinomie russellienne par Le´sniewskiLe´sniewski, Methodos, vol.1, pp.237-257, 1949.

, Le´sniewskiLe´sniewski's Systems: Ontology and Mereology, 1984.

, Le´sniewskiLe´sniewski's Systems: Protothetic, 1998.

A. Tarski, On the Primitive Term of Logistic, Logic, Semantics, Metamathematics. Papers from 1923 to 1938, pp.1-23, 1923.

R. Urbaniak, Le´sniewskiLe´sniewski's Systems of Logic and Foundations of Mathematics, 2014.

D. Dubois, E. Lorini, and &. Prade, The Strength of Desires: a Logical Approach, Minds and Machines, forthcoming

E. Lorini, A logic for reasoning about moral agents, Logique et Analyse, vol.58, pp.177-218, 2016.

E. Lorini and &. Herzig, A logic of intention and attempt, Synthese, vol.163, issue.1, pp.45-77, 2008.

M. Couceiro, N. Hug, H. Prade, and &. G. Richard, Analogy-preserving functions: a way to extend Boolean samples, 26th International Joint Conference on Artificial Intelligence, IJCAI'17, pp.1575-1581, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01668230

D. Dubois, H. Prade, and &. G. Richard, Multiple-valued extensions of analogical proportions, Fuzzy Sets and Systems, vol.292, pp.193-202, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01475021

S. Klein, Analogy and mysticism and the structure of culture, Current Anthropology, vol.24, issue.2, pp.151-180, 1983.

, Logic and Philosophy of Religion, Special Issue of Sophia, vol.56, issue.2, 2017.

R. Silvestre and &. Beziau, Logic and Philosophy of Religion, vol.56, pp.139-145, 2017.

J. Sobel, Logic and Theism: Arguments for and against Beliefs in God, 2004.

C. Taliaferro, P. Draper, and &. P. Quinn, The Blackwell Companion to the Philosophy of Religion, 2010.

N. Trakakis, Useful Links ˆ Anselm: Ontological Argument for God's Existence, Internet Encyclopedia of Philosophy ˆ World Congresses on Logic and Religion Bibliography ˆ On Wittgenstein's Logic in the Tractatus, 2007.

E. Anscombe, An Introduction to Wittgenstein's Tractatus, 1959.

R. J. Fogelin, R. Wittgenstein, and . Paul, , 1976.

P. Frascolla, Understanding Wittgenstein's Tractatus, Routledge, 2006.

S. Shanker, Wittgenstein and the Turning Point in the Philosophy of Mathematics, 1987.

S. Toulmin, &. Janik, &. Wittgenstein, S. Vienna, and . Schuster, , 1973.

L. Wittgenstein, C. ;. Wittgenstein's-lectures, D. Lee, &. Rowman, . Littlefield et al., ˆ On semantic technologies 1. D.B. Lenat & R.V. Guha, Building Large Knowledge-Based Systems: Representation and Inference in the Cyc Project, pp.1930-1932, 1980.

S. Nirenburg-&-v.-raskin, Ontological Semantics, 2004.

J. Sowa, Knowledge Representation: Logical, Philosophical and Computational Foundations, 2000.

E. Thomsen, OLAP Solutions: Building Multidimensional Information Systems, 2002.

M. Krynicki, J. Tomasik, and &. Zdanowski, Theories of initial segments of standard models of arithmetics and their complete extensions, Theoretical Computer Science, vol.412, issue.31, pp.3975-3991, 2011.

M. Kokar, J. Tomasik, and &. Weyman, Formalizing classes of information fusion systems, Information Fusion, vol.5, issue.3, pp.189-202, 2004.

J. A. Tomasik, Discrete dynamic approach to multisensory multitrack fusion, Aerosense 2000: Signal and Image Processing, vol.4051, pp.369-379, 2000.
DOI : 10.1117/12.381651

J. A. Tomasik, Synthesis theories versus semantics integration for complex situation assessment, 8th NATO Military Sensing Symposium, vol.169, 2011.

B. V. Dasarathy, Metric sensitivity of reciprocal relationship bonds in the knowledge discovery process, Data Mining and Knowledge Discovery: Theory, Tools, and Technology II, vol.4057, 2000.

W. A. Sander, Information Fusion, International Military and Defense Encyclopedia, vol.3, pp.1259-1265, 1993.

C. C. Chang-&-h and . Keisler, Model Theory, 1990.

W. Hodges, Model Theory, 1993.

I. G. Bashmakova, The Arithmetic Books of Euclid's Elements, Istoriko-matemati?eskie issledovaniya, vol.I, p.321, 1948.

, Ancient Logic and Its Modern Interpretations, D. Reidel, 1974.

G. Fine, Aristotle's Criticism of Plato's Theory of Forms, 1993.

H. , Zur Geschichte der vollständigen Induktion, Archive Internationale d'Histoire des Sciences, vol.6, pp.17-37, 1953.

J. Gardies, Le raisonnement par l'absurde, 1991.

A. F. Losev, History of Ancient Aesthetics (in Russian), 7 volumes, pp.1963-1988

I. Mueller, Philosophy of Mathematics and Deductive Structure in Euclid's "Elements, 1981.

F. J. Pelletier-&-e and . Zalta, How to Say Goodbye to the Third Man, Nous, vol.34, issue.2, pp.165-202, 2000.

I. Vandoulakis, Was Euclid's Approach to Arithmetic Axiomatic?, Oriens-Occidens, Cahiers du Centre d'Histoire des Sciences et des Philosophies Arabes et Médiévales, vol.2, pp.141-181, 1998.

I. Vandoulakis, Styles of Greek arithmetic reasoning, Study of the History of Mathematics, pp.12-22, 2009.

I. Vandoulakis, Plato's Third Man Paradox: its Logic and History, Archives Internationale d'Histoire des Sciences, vol.59, pp.3-53, 2009.
DOI : 10.1484/j.arihs.5.101823

I. Vandoulakis, A Generic Interpretation of Neo-Pythagorean Arithmetic, Sciences et des Philosophies Arabes et Médiévales, vol.7, pp.113-154, 2010.

G. Vlastos, The Third Man Argument in the Parmenides, Philosophical Review, vol.63, pp.319-349, 1954.

U. Link, ˆ. Pelletier, &. Edward, and N. Zalta, How to Say Goodbye to the Third Man

J. A. Blair, Relevance, Acceptability and Sufficiency Today, Groundwork in the Theory of Argumentation, pp.87-100, 2012.
DOI : 10.1007/978-94-007-2363-4_8

A. Corner and &. Hahn, Normative theories of argumentation: Are some norms better than others?, Synthese, vol.190, issue.16, pp.3579-3610, 2013.

F. H. Van-eemeren, Extending the pragma-dialectical theory of argumentation, John Benjamins, 2010.

F. H. Van-eemeren and &. R. Grootendorst, A systematic theory of argumentation: the pragma-dialectical approach, 2004.

D. Godden and &. Zenker, Denying antecedents and affirming consequents: The state of the art, Informal Logic, vol.35, issue.1, pp.88-134, 2015.

D. Godden and &. Zenker, A probabilistic analysis of argument cogency, Synthese, vol.195, issue.4, pp.1715-1740, 2018.

U. Hahn and &. Hornikx, A normative framework for argument quality: Argumentation schemes with a Bayesian foundation, Synthese, vol.193, issue.6, pp.1833-1873, 2016.
DOI : 10.1007/s11229-015-0815-0

U. Hahn and &. Oaksford, A Bayesian Approach to Informal Argument Fallacies, Synthese, vol.152, issue.2, pp.207-236, 2006.
DOI : 10.1007/s11229-005-5233-2

U. Hahn and &. Oaksford, A normative theory of argument strength, Informal Logic, vol.26, issue.1, pp.1-24, 2006.

C. Hamblin, Fallacies, 1970.

R. Johnson, Manifest rationality: A pragmatic theory of argument, 2000.

K. Korb, Bayesian informal logic and fallacy, Informal Logic, vol.24, issue.1, pp.41-70, 2004.
DOI : 10.22329/il.v24i1.2132

URL : https://informallogic.ca/index.php/informal_logic/article/download/2132/1576

C. Lumer, Pragma-Dialectics and the Function of Argumentation, Argumentation, vol.24, issue.1, pp.41-69, 2010.

M. Oaksford and &. Hahn, A Bayesian approach to the argument from ignorance, Canadian Journal of Experimental Psychology, vol.58, issue.2, pp.75-85, 2004.

H. Siegel and &. Biro, Epistemic Normativity, Argumentation, and Fallacies, Argumentation, vol.11, issue.3, pp.277-292, 1997.

D. N. Walton, A Pragmatic Theory of Fallacy, 1995.

D. N. Walton, Why Fallacies Appear to be Better Arguments Than They Are, Informal Logic, vol.30, issue.2, pp.159-184, 2010.
DOI : 10.22329/il.v30i2.2868

URL : https://informallogic.ca/index.php/informal_logic/article/download/2868/2407

D. N. Walton, C. Reed, and &. Macagno, Argumentation Schemes, 2008.

J. Woods, How philosophical is informal logic?, Informal Logic, vol.20, issue.2, pp.139-167, 2000.
DOI : 10.22329/il.v20i2.2266

URL : https://informallogic.ca/index.php/informal_logic/article/download/2266/1710

J. Woods, Errors of Reasoning: Naturalizing the Logic of Inference, 2013.

J. Woods, Epistemology Mathematicized, vol.33, issue.2, pp.292-331, 2013.

F. Zenker, Proceedings of the International Society for the Study of Argumentation, pp.1581-1589, 1984.

F. Zenker, The polysemy of 'fallacy' -or 'bias', for that matter, Argumentation, Objectivity and Bias, Proceedings of the 11th Conference of the Ontario Society for the Study of Argumentation, pp.1-14, 2016.

P. Dung, On the Acceptability of Arguments and its Fundamental Role in Non-Monotonic Reasoning, Logic Programming and n-Person Games, Artificial Intelligence, vol.88, pp.321-357, 1995.

L. Amgoud and &. Ben-naim, Axiomatic foundations of acceptability semantics, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning, pp.2-11, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01531176

K. Apel and C. Peirce, From Pragmatism to Pragmaticism, 1995.

S. Brier, Cybersemiotics: why information is not enough, p.13, 2008.

S. Brier, Can Biosemiotics be a "Science" if its Purpose is to be a Bridge between the Natural, Social and Human Sciences?, Progress in Biophysics and Molecular Biology, vol.119, issue.3, pp.576-587, 2015.

S. Brier, How to Produce a Transdisciplinary Information Concept for a Universal Theory of Information?, Information Studies and the Quest for Transdisciplinarity: Unity through Diversity, vol.9, pp.11-58, 2017.

, Peirce and Biosemiotics: A Guess at the Riddle of Life, Biosemiotics series, vol.1, 2014.

B. Coecke and &. Kissinger, Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning, 2017.
DOI : 10.1017/9781316219317

B. Coecke, Quantum picturalism, Contemporary Physics, vol.51, issue.1, pp.59-83, 2010.
DOI : 10.1080/00107510903257624

URL : http://arxiv.org/pdf/0908.1787

B. Coecke and &. S. Gogioso, Quantum theory in Pictures, Top Secret

B. Coecke and &. S. Gogioso, Quantum theory in Hilbert space

D. Dubois, J. Lang, and &. Prade, Possibilistic logic, Handbook of Logic in Artificial Intelligence and Logic Programming, vol.3, pp.439-513, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00867738

D. Ciucci and &. Dubois, A modal theorem-preserving translation of a class of three-valued logics of incomplete information, Journal of Applied Non-Classical Logics, vol.23, issue.4, pp.321-352, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01122841

M. Banerjee and &. Dubois, A simple logic for reasoning about incomplete knowledge, International Journal of Approximate Reasoning, vol.55, pp.639-653, 2014.
DOI : 10.1016/j.ijar.2013.11.003

URL : https://hal.archives-ouvertes.fr/hal-01119806

D. Ciucci and &. Dubois, A Two-Tiered Propositional Framework for Handling Multisource Inconsistent Information, European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, pp.398-408, 2017.

D. Dubois, H. Prade, and &. S. Schockaert, Generalized possibilistic logic: Foundations and applications to qualitative reasoning about uncertainty, Artificial Intelligence, vol.252, pp.139-174, 2017.

A. Bacon, Non-classical Metatheory for Non-classical Logics, Journal of Philosophical Logic, vol.42, pp.335-355, 2012.

M. K. Chakraborty, Graded consequence: further studies, Journal of Applied Non-Classical Logics, vol.5, pp.227-237, 1995.

A. Church, Introduction to Mathematical Logic, vol.1, 1956.

G. Malinowski, Inferential many-valuedness, Philosophical Logic in Poland, pp.75-84, 1994.

R. Parikh, The Problem of Vague Predicates, Language, Logic, and Method, pp.241-261, 1983.

C. Pelta, Wide sets, deep many-valuedness and sorites arguments, Mathware & Soft Computing, vol.11, pp.5-11, 2004.

T. Vetterlein, F. Esteva, and &. Godo, Logics for Approximate Entailment in ordered universes of discourse, International Journal of Approximate Reasoning, vol.71, pp.50-63, 2016.

S. S. Goncharov-&-d and . Sviridenko, ?-Programming, American Mathematical Society Translations: Series, vol.2, pp.101-121, 1989.

S. S. Goncharov-&-d and . Sviridenko, Theoretical aspects of ?-programming, Lecture Notes in Computer Science, vol.215, pp.169-179, 1986.

Y. L. Ershov, S. S. Goncharov-&-d, and . Sviridenko, Semantic programming, Information Processing 86: Proceedings of the IFIP 10th World Computer Congress, vol.10, pp.1093-1100, 1986.

S. S. Goncharov-&-d and . Sviridenko, Mathematical bases of semantic programming, Soviet Mathematics Doklady, vol.31, issue.6, pp.608-610, 1986.

Y. L. Ershov, S. S. Goncharov-&-d, and . Sviridenko, Semantic foundations of programming, Fundamentals of Computation Theory: Proceedings of International Conference on FCT 87, vol.278, pp.116-122, 1987.

Y. L. Ershov, The principle of ?-enumeration, Soviet Mathematics Doklady, vol.27, pp.670-672, 1983.

Y. L. Ershov, Definability and Computability, Siberian School of Algebra and Logic, 1996.

S. S. Goncharov, Conditional Terms in Semantic Programming, Siberian Mathematical Journal, vol.58, 2017.

R. Krömer, Tool and object. A history and philosophy of category theory, 2007.

K. Manders, Diagram-Based Geometric Practice" and "The Euclidean Diagram, The Philosophy of Mathematical Practice, vol.3, pp.80-133, 1995.

M. Baaz and &. Leitsch, Cut-elimination and redundancy-elimination by resolution, Journal of Symbolic Computation, vol.29, pp.149-176, 2000.

M. Baaz, S. Hetzl, A. Leitsch, C. Richter, and &. Spohr, CERES: an analysis of Fürstenberg's proof of the infinity of primes, Theoretical Computer Science, vol.403, pp.160-175, 2008.

, * Keynote speaker at the workshop "Proof Theory

P. M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming, and n-person games, Artificial Intelligence, vol.77, pp.321-357, 1995.

H. Prakken and &. Vreeswijk, Logic for Defeasible Argumentation', in Handbook of Philosophical Logic, vol.4, pp.218-319, 2002.

E. Lisanyuk, Argumentation, R. Pavilionis's Meaning Continuum and the Kitchen Debate, Problemos, vol.88, pp.218-319, 2015.

M. Caminada and &. Amgoud, On the evaluation of argumentative formalisms, Artificial Intelligence, vol.171, issue.5-6, pp.286-310, 2007.

V. Finn, Research and technology information, series 2: Information processes and systems, vols. 5-6, pp.3-19, 1996.

D. Bochvar, On a three-valued calculus and its application to the paradoxes of the extended classical functional calculus, Mathematical Collection, vol.4, issue.2, p.1938

G. Frege, Conceptual Notation: A Formula Language of Pure Thought Modeled upon the Formula Language of Arithmetic, Begriffsschrift, first published in 1879, 1972.

G. Frege, Die Grundlagen der Arithmetik, first published in 1884, English version: Foundations of Arithmetic, 1980.

C. Peirce, The Logic of Mathematics in Relation to Education, Philosophy of Mathematics: Selected Writings, 2010.

C. Peirce and ;. Lukasiewicz, O logice trójwarto´trójwarto´sciowej, Philosophy of Mathematics: Selected Writings, vol.5, pp.87-88, 1920.

J. Lukasiewicz, Selected Works, 1970.

G. Malinowski, The Many Valued and Nonmonotonic Turn in Logic, Handbook of the History of Logic, vol.8, pp.13-94, 2007.

K. R. Popper, The Logic of Scientific Discovery, 1959.

C. Hempel, Selected Philosophical Essays, 2000.

I. Lakatos, Falsification and the Methodology of Scientific Research Programmes, Proceedings of the International Colloquium in the Philosophy of Science: Criticism and the Growth of Knowledge, vol.4, pp.91-196, 1970.

L. Laudan, Progress and its problems: Towards a theory of scientific growth, 1977.

J. Smith, Inconsistencies and scientific reasoning, Studies in History and Philosophy of Science, vol.4, issue.19, pp.429-445, 1988.

J. Meheus, How to reason sensibly yet naturally from inconsistencies", in Inconsistency in science, pp.151-164, 2010.

N. Rescher-&-r and . Manor, On inference from inconsistent premises, Theory and decision, vol.1, issue.2, pp.179-217, 1970.

D. Batens, Towards the Unification of Inconsistency Handling Mechanisms, Logic and Logical Philosophy, vol.8, pp.5-31, 2000.

D. Batens, Pluralism in Scientific Problem Solving. Why Inconsistency is No Big Deal, Humana.Mente Journal of Philosophical Studies, vol.32, pp.149-177, 2017.

B. Brown and &. Priest, Chunk and Permeate, a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus, Journal of Philosophical Logic, vol.33, issue.4, pp.379-388, 2004.
DOI : 10.1023/b:logi.0000036831.48866.12

B. Brown and &. Priest, Chunk and permeate II: Bohr's hydrogen atom, European Journal for Philosophy of Science, vol.5, issue.3, pp.297-314, 2015.
DOI : 10.1007/s13194-014-0104-7

B. Brown, On the Preservation of Reliability, Logical Studies of Paraconsistent Reasoning in Science and Mathematics, pp.65-80, 2016.

B. Brown, Pluralistic Models and Reasoning in Climate Science, Humana.Mente Journal of Philosophical Studies, vol.32, pp.179-194, 2017.

O. Bueno, Scientific Pluralism, Consistency Preservation, and Inconsistency Toleration, Humana.Mente Journal of Philosophical Studies, vol.32, pp.229-245, 2017.

D. W. Miller, Reconditioning the Conditional, Conceptual Clarifications. Tributes to Patrick Suppes, vol.23, pp.9-27, 1922.

D. W. Miller-&-k and . Popper, Deductive Dependence, Actes IV CongrésCataì a de L` ogica, pp.21-29, 1986.

A. Moktefi, Beyond syllogisms: Carroll's (marked) quadriliteral diagram, Visual Reasoning with Diagrams, pp.55-71, 2013.
DOI : 10.1007/978-3-0348-0600-8_4

L. Carroll, Lewis Carroll's Symbolic Logic, 1986.

F. Abeles, The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces, 2010.

A. Moretti, Was Lewis Carroll an amazing oppositional geometer?, History and Philosophy of Logic, vol.35, pp.383-409, 2014.
DOI : 10.1080/01445340.2014.981022

E. Amiot, Music Through Fourier Space: Discrete Fourier Transform in Music Theory, 2016.

R. Carnap and W. Der-logische-aufbau-der, English version: The Logical Structure of the World. Pseudoproblems in Philosophy, 1928.

T. Noll, The Topos of Triads, Colloquium on Mathematical Music Theory, Grazer Mathematische Berichte, vol.347, pp.1-26, 2005.

S. Russell and &. Norvig, Artificial Intelligence: A Modern Approach, 1995.

J. , A Stroll Through the Worlds of Animals and Men: A Picture Book of Invisible Worlds, Instinctive Behavior: The Development of a Modern Concept, pp.5-80, 1957.

D. Hilbert, Grundlagen der Geometrie, Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, edited by the FestComitee, p.1899

D. Hilbert, Logische Principien des mathematischen Denkens, lecture summer semester, 1905.

D. Hilbert-&-w.-ackermann, Grundzüge der theoretischen Logik, 1928.

F. Correia, Logical Grounds, Review of Symbolic Logic, vol.7, pp.31-59, 2014.

K. Fine, The pure logic of ground, Review of Symbolic Logic, vol.25, pp.1-25, 2012.

J. Korbmacher, Axiomatic Theories of Partial Grounds, Journal of Philosophical Logic, vol.35, pp.1-31, 2017.

B. Schnieder, A logic for 'Because', Review of Symbolic Logic, vol.4, pp.445-465, 2011.

, * Keynote speaker at the workshop "Proof Theory

F. Boas, The Mind of Primitive Man, 1911.

I. Kant and . Logic, , 1974.

C. Lévi-strauss, The Savage Mind, 1966.

L. Lévy-bruhl, How Natives Think, 1925.

H. L. Morgan, Ancient Society, p.1877

J. Royce, The Principles of Logic", in Royce's Logical Essays: Collected Logical Essays of Josiah Royce

B. Whorf, Science and Linguistics, Technology Review, vol.44, pp.247-248, 1940.

C. Babbage, Observations on the notation employed in the calculus of functions, Transactions of the Cambridge Philosophical Society, vol.I, pp.63-76, 1821.

C. Babbage, On the influence of signs in mathematical reasoning, Transactions of the Cambridge Philosophical Society, vol.II, pp.325-377, 1827.

C. Babbage, On notations, Edinburgh Encyclopedia, vol.15, pp.394-399, 1830.

H. , The calculus of equivalent statements II, Proceedings of the London Mathematical Society, vol.9, pp.177-186, 1878.

H. , On the diagrammatic and mechanical representation of propositions and reasoning, Journal of Science, vol.10, pp.276-279, 1880.

L. Couturat, , vol.87

, Mathé-matiques, langage, philosophie, Classiques Garnier, pp.1868-1914, 2017.

B. Russell, Correspondance avec Louis Couturat sur la Philosophie, la Logique et la Politique (1897-1913), Edition and notes by AnneFrançoise Schmid, Kimé, vol.735, 2001.

A. Schmid, La Controverse entre Bertrand Russell et Henri Poincaré, Dimensions of Logical Concepts, Coleção CLE book series, vol.54, 2009.
DOI : 10.1111/j.1746-8361.1983.tb00824.x

A. Schmid, Méditation sur la clause finale, Construction: Festschrift for Gerhard Heinzmann, pp.75-84, 2010.

A. J. Ayer, Language, Truth and Logic, 1946.

P. Geach, Logic Matters, 1972.

W. V. Quine, Philosophy of Logic, 1970.

, Keynote speaker at the workshop "Reflections on Paraconsistency

G. Frege, Gefankengefüge, Beiträge zur Philosophie des deutschen Idealismus, vol.3, pp.36-51, 1923.

P. Schroeder-heister, Validity Concepts in Proof-theoretic Semantics, vol.148, pp.525-571, 2006.

G. Sundholm, Inference versus consequence" revisited: Inference, consequence, conditional, implication, Synthese, vol.187, issue.3, pp.943-956, 2012.
DOI : 10.1007/s11229-011-9901-0

URL : https://link.springer.com/content/pdf/10.1007%2Fs11229-011-9901-0.pdf

G. Sundholm, The Neglect of Epistemic Considerations in Logic. The Case of Epistemic Assumptions, 2017.

A. Tarski, On the Concept of Following Logically, History and Philosophy of Logic, vol.23, pp.155-196, 2002.

, Keynote speaker at the workshop "Naming Logics II

B. Nuseibeh, S. Easterbrook, and &. Russo, Making Inconsistency Respectable in Software Development, Journal of Systems and Software, vol.58, issue.2, pp.171-180, 2001.
DOI : 10.1016/s0164-1212(01)00036-x

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.3300

N. Ernst, A. Borgida, J. Mylopoulos, and &. Jureta, Agile Requirements Evolution via Paraconsistent Reasoning, Proceedings of the 24th International CAiSE *, pp.382-397, 2012.
DOI : 10.1007/978-3-642-31095-9_25

A. Finkelstein, D. Gabbay, A. Hunter, J. Kramer, and &. Nuseibeh, Inconsistency Handling in Multiperspective Specifications, IEEE „ Transactions on Software Engineering, vol.20, pp.569-578, 1994.
DOI : 10.1109/32.310667

URL : http://spiral.imperial.ac.uk/bitstream/10044/1/460/1/Inconsistency%20handling%20in%20multiperspective%20specifications.pdf

I. Hadar and &. Zamansky, When a Paradigm is Inconsistent with Intuition: The Case of Inconsistency Management, Proceedings of 3rd International Workshop on COGNISE , Lecture Notes in Business Information Processing, vol.215, pp.107-113, 2015.

I. Hadar and &. Zamansky, Cognitive Factors in Inconsistency Management, Proceedings of 23rd IEEE § International Requirements Engineering Conference, pp.226-229, 2015.
DOI : 10.1109/re.2015.7320427

A. Zamansky, I. Hadar, and &. D. Berry, Reasoning about Inconsistency in RE ¶ : Separating the Wheat from the Chaff, Proceedings of the 11th International Conference on ENASE †, pp.377-382, 2016.

A. Moretti, Arrow Hexagons, The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol.II, pp.417-489, 2015.
DOI : 10.1007/978-3-319-15368-1_20

H. Schepers, Logisches Quadrat, Historisches Wörterbuch der Philosophie, vol.7, pp.1733-1736, 1971.

U. O'meadhra, Medieval Logic Diagrams in Bro Church, Gotland, Sweden, Acta Archaeologica, vol.83, issue.1, pp.287-316, 2012.

A. Moretti, The Geometry of Logical Opposition, 2009.

A. Geulincx, De Cubo Logico, Methodus inveniendi argumenta, quae solertia quibusdam dicitur, p.1675

A. Morgan, Logical Bibliography, Notes and Queries, vol.3, issue.6, pp.101-104

A. Costa-leite, Opposition in a line segment, 2016.

F. Schang, An Arithmetization of Logical Oppositions, The Square of Opposition: A Cornerstone of Thought, pp.215-237, 2017.

H. Smessaert and &. Demey, Logical Geometries and Information in the Square of Oppositions, Journal of Logic, Language and Information, vol.23, issue.4, pp.527-565, 2014.

P. Hinst, Pragmatische Regeln des logischen Argumentierens, Logik und Pragmatik. Zum Rechtfertigungsproblem logischer Sprachregeln, pp.199-215, 1982.

F. Reinmuth, , 2014.

F. Reinmuth and &. Cordes, Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction, Logic and Logical Philosophy, vol.26, issue.2, pp.163-196, 2017.

C. and D. Novaes, Toward a Practice-Based Philosophy of Logic: Formal Languages as a Case Study, Philosophia Scientiae, vol.16, issue.1, pp.71-102, 2012.

A. Moktefi and &. Shin, Logic: A History of its Central Concepts, Handbook of the History of Logic, vol.11, pp.611-682, 2012.

H. Smessaert and &. Demey, Logical Geometries and Information in the Square of Oppositions, Journal of Logic, Language and Information, vol.23, issue.4, pp.527-565, 2014.

G. Frege, Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, L. Nebert, p.1879

G. Landini, Frege's Notations: What They Are and How They Mean, 2012.

D. Macbeth, Frege's Logic, 2005.

D. Schlimm, Frege's Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs, History and Philosophy of Logic, vol.39, issue.1, pp.53-79, 2018.

G. Gentzen, UntersuchungenüberUntersuchungen¨Untersuchungenüber das logische Schließen, Mathematische Zeitschrift, vol.39, pp.405-431, 1935.

G. Gentzen, ¨ Uber die Existenz unabhängiger Axiomensystem zu unendlichen Satzsystemen, Mathematische Annalen, vol.107, pp.329-350, 1933.
DOI : 10.1007/bf01448897

P. Hertz, ¨ Uber Axiomensysteme für beliebige Satzsysteme. I Teil
DOI : 10.1007/bf01459067

G. Sätze-ersten, Mathematische Annalen, vol.87, pp.246-269, 1923.

P. Hertz, ¨ Uber das Wesen der Logik und der logischen Urteilsformen, Abhandlungen der Fries'schen Schule, vol.6, pp.227-272, 1935.

, Truth-tables and Tautologies in Early Logical Empiricism

W. N. Goldfarb-;-r and . Giere, of Minnesota Studies in the Philosophy of Science series, The Philosophy of Mathematics in Early Positivism, vol.16, pp.213-230, 1996.

W. Goldfarb, On Gödel's Way in: The Influence of Rudolf Carnap, The Bulletin of Symbolic Logic, vol.11, pp.185-193, 2005.

W. Goldfarb and &. Ricketts, Wissenschaft und Subjektivität -Der Wiener Kreis und die Philosophie des 20. Jahrhunderts, pp.61-78, 1992.

T. Ricketts, Carnap's Principle of Tolerance, Empiricism, and Conventionalism, pp.176-200, 1992.

T. Uebel, Learning Logical Tolerance: Hans Hahn on the Foundations of Mathematics, vol.26, pp.175-209, 2007.

T. Uebel, Carnap's Logical Syntax in the Context of the Vienna Circle, Carnap's Logical Syntax of Language, pp.53-78, 2009.

K. Gödel, Is mathematics syntax of language?, Collected Works: Volume III: Unpublished essays and lectures, pp.334-363, 1953.

M. Black, A Companion to Wittgenstein's Tractatus, 1964.

L. Wittgenstein, Tractatus Logico-Philosophicus, 2005.

R. B. Brandom, Making It Explicit: Reasoning, Representing, and Discursive Commitment, 1994.

R. B. Brandom, Articulating reasons: an introduction to inferentialism, 2000.

R. B. Brandom, Between saying and doing: towards an analytic pragmatism, 2008.

W. De-campos-sanz and &. T. Piecha, Inversion by definitional reflection and the admissibility of logical rules, Review of Symbolic Logic, vol.2, issue.3, pp.550-569, 2009.

M. N. Lance and &. Kremer, The logical structure of linguistic commitment 1: Four systems of non-relevant commitment entailment, Journal of Philosophical Logic, vol.23, issue.4, pp.369-400, 1994.

B. Nickel, Dynamics, Brandom-style, Philosophical Studies, vol.162, issue.2, pp.333-354, 2013.
DOI : 10.1007/s11098-011-9768-4

URL : https://dash.harvard.edu/bitstream/1/13041028/1/brandom-dynamics-plain.pdf

J. Peregrin, Inferentialism: why rules matter, 2014.

T. Piecha and &. Schroeder-heister, Atomic systems in proof-theoretic semantics: Two approaches, Epistemology, Knowledge and the Impact of Interaction, pp.47-62, 2016.

P. Piwek, Towards a computational account of inferentialist meaning, Proceedings of the 50th Anniversary Convention of the AISB *, 2014.

T. Sandqvist, Base-extension semantics for intuitionistic sentential logic, Logic Journal of the IGPL „, vol.23, issue.5, pp.719-731, 2015.

T. Sandqvist, Hypothesis-Discharging Rules in Atomic Bases, 2015.

P. Schroeder-heister, Generalized definitional reflection and the inversion principle, Logica Universalis, vol.1, issue.2, pp.355-376, 2007.

P. Schroeder-heister, Definitional reflection and basic logic, Annals of Pure and Applied Logic, vol.164, issue.4, pp.491-501, 2013.

G. R. Renardel-de-lavalette, Interpolation in propositional Horn logic, Journal of Logic and Computation

B. Möller, Kleene getting lazy, Science of Computer Programming, vol.65, issue.2, pp.195-214, 2007.

D. J. Hughes, Proofs without Syntax, Annals of Mathematics, vol.164, issue.3, pp.1065-1076, 2006.

D. J. Hughes, Towards Hilbert's 24th problem: Combinatorial Proof Invariants: (preliminary version), Electronic Notes in Theoretical Computer Science, vol.165, pp.37-63, 2006.

L. Straßburger, Combinatorial Flows and Proof Compression, 2017.

L. Straßburger, Combinatorial Flows and Their Normalisation, Conference on Formal Structures for Computation and Deduction, LIPIcs * book series, vol.84, pp.1-31, 2017.

, * Leibniz International Proceedings in Informatics

W. E. Johnson, Logic: Part 1, 1921.

M. Matthen, Seeing, Doing and Knowing. A Philosophical Theory of Sense Perception, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00692045

W. Sellars, Action, Knowledge and Reality: Studies in Honor of Wilfrid Sellars, pp.295-347, 1975.

, Lecture I: Perception; Lecture II: Minds; Lecture III

D. Huron, Sweet Anticipation: Music and the Psychology of Expectation, 2006.

, Handbook of Music and Emotion, 2010.

V. Kolman, Emotions and Understanding in Music, Idealistic Studies, vol.44, issue.1, pp.83-100, 2014.

V. Kolman, Normative Pragmatism and the Language Game of Music, Contemporary Pragmatism, vol.11, issue.2, pp.147-163, 2014.

V. Kolman, Hegel's 'Bad Infinity' as a Logical Problem, Hegel Bulletin, vol.37, issue.2, pp.258-280, 2016.

L. Meyer, Emotion and Meaning in Music, 1956.

J. Harrington, Time: A Philosophical Introduction, 2015.

J. E. Mctaggart, The unreality of time, vol.17, pp.457-474, 1908.

A. Popoff, M. Andreatta, and &. Ehresmann, A Categorical Generalization of Klumpenhouwer Networks, Mathematics and Computation in Music: 5th International Conference, pp.303-314, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01263398

N. Rossiter, M. Heather, and &. Brockway, Monadic Design for Universal Systems, ANPA * Proceedings 37 & 38, pp.369-399, 2018.

A. Bergson, A reformulation of certain aspects of welfare economics, The Quarterly Journal of Economics, vol.52, issue.2, pp.310-334, 1938.

P. A. Samuelson, Foundations of Economic Analysis, p.216, 1947.

R. Giovagnoli, Life-world, Language and Religion. Habermas' Perspective, Aquinas, vol.58, issue.1-2, pp.253-260, 2015.

R. Giovagnoli, Communicative Life-world and Religion, Asian Research Journal of Arts and Social Sciences, vol.1, issue.3, pp.1-7, 2016.

R. Giovagnoli, Habits and Rituals, Proceedings of the IS4SI *, 2017.

R. Giovagnoli, Lifeworld, We-Intentionality and Rituals, Mind, Collective Agency, pp.22-32, 2017.

R. Giovagnoli, The Function of Language for the problem of Representation, Representation and Reality. Humans, Other Living Beings and Intelligent Machines, pp.235-246, 2017.

A. , Habits, Rituals and the Evaluative Brain, Annual Review of Neuroscience, vol.31, pp.359-387, 2008.

J. Habermas, Nachmetaphysisches Denken II: Aufsätze und Repliken, * International Society for the Study of Information

A. , The Nicomachean Ethics, 1975.

H. Collins, Tacit and Explicit Knowledge, 2012.

A. Goldman, Experts. Which ones should you trust?, Philosophy and Phenomenological Research, vol.63, issue.1, pp.85-110, 2011.

, Phronesis as Professional Knowledge: Practical Wisdom in the Professions, 2012.

M. Van-manen, Phenomenology of Practice: Meaning-Giving Methods in Phenomenological Research and Writing, 2014.

J. Woods, Errors of Reasoning. Naturalizing the Logic of Inference, 2013.

S. Arfini and &. Magnani, An eco-cognitive model of ignorance immunization, Philosophy and Cognitive Science II. Western & Eastern Studies, 2015.

L. Magnani, Understanding Violence. The Intertwining of Morality, Religion and Violence: A Philosophical Stance, 2011.

J. R. Searle, The Construction of Social Reality, Penguin Books, 1995.

M. Ferraris, Documentality: Why it is Necessary to Leave Traces, 2013.

T. R. , Schatzki Social Practices: A Wittgensteinian Approach to Human Activity and the Social, 1996.

M. Vicario, A. Bessi, and F. Zollo, The spreading of misinformation online, PNAS *, vol.113, issue.3, pp.554-559, 2016.

F. Zollo, P. K. Novak, and M. D. Vicario, Emotional dynamics in the age of misinformation, PLoS „ ONE, vol.10, issue.9, 2015.

F. Zollo, A. Bessi, and M. D. Vicario, Debunking in a world of tribes, PLoS ONE, vol.12, issue.7, 2017.

M. Vicario, F. Zollo, and G. Caldarelli, Mapping social dynamics on Facebook: The Brexit debate, Social Newtorks, vol.50, pp.6-16, 2017.

A. L. Schmidt, F. Zollo, and M. D. Vicario, Anatomy of news consumption on Facebook, PNAS, vol.114, issue.12, pp.3035-3039, 2017.

G. H. Wright, The Logic of Preference, 1963.

A. N. Prior, Tense-logic and the continuity of time, Studia Logica, vol.13, issue.1, pp.133-151, 1962.

J. A. Goguen-&-r and . Burstall, Institutions: Abstract model theory for specification and programming, Journal of the ACM *, vol.39, issue.1, pp.95-146

H. Halvorson, What Scientific Theories Could Not Be, Philosophy of Science, vol.79, issue.2, pp.183-206

H. D. Macpherson, D. Marker, and &. Steinhorn, Weakly o-minimal structures and real closed fields, Transactions of The American Mathematical Society, vol.352, issue.12, pp.5435-5483, 2000.

B. S. Baizhanov, Expansion of a model of a weakly o-minimal theory by a family of unary predicates, The Journal of Symbolic Logic, vol.66, issue.3, pp.1382-1414, 2001.

B. Sh and . Kulpeshov, Weakly o-minimal structures and some of their properties, The Journal of Symbolic Logic, vol.63, issue.4, pp.1511-1528, 1998.

S. Ghilardi, Unification Through Projectivity, Journal of Logic and Computation, vol.7, issue.6, pp.733-752, 1997.
DOI : 10.1093/logcom/7.6.733

R. Iemhoff, On the admissible rules of intuitionistic propositional logic, The Journal of Symbolic Logic, vol.66, issue.1, pp.281-294, 2001.

S. S. Goncharov-&-v and . Dzgoev, Autostability of models, Algebra and Logic, vol.19, issue.1, pp.28-37, 1980.

B. Khoussainov and &. Kowalski, Computable isomorphisms of Boolean algebras with operators, Studia Logica, vol.100, issue.3, pp.481-496, 2012.

D. R. Hirschfeldt, B. Khoussainov, R. A. Shore-&-a, and . Slinko, Degree spectra and computable dimensions in algebraic structures, Annals of Pure and Applied Logic, vol.115, issue.1-3, pp.71-113, 2002.

N. Bazhenov, Categoricity spectra for polymodal algebras, Studia Logica, vol.104, issue.6, pp.1083-1097, 2016.
DOI : 10.1007/s11225-016-9667-y

G. Dimov and &. Vakarelov, Contact Algebras and Region-based Theory of Space: A Proximity Approach -I, Fundamenta Informaticae, vol.74, issue.2-3, pp.209-249, 2006.

M. V. Sapir, The lattice of quasivarieties of semigroups, Algebra Universalis, vol.21, pp.172-180, 1985.

A. M. Nurakunov, Unreasonable lattices of quasivarieties, International Journal of Algebra and Computation, vol.22, issue.3, pp.1-17, 2012.

M. Schwidefsky-&-a.-zamojska-dzienio, Lattices of subclasses. II, International Journal of Algebra and Computation, vol.24, issue.8, pp.1099-1126, 2014.

M. Schwidefsky, Complexity of quasivariety lattices, Algebra Logika, vol.54, issue.3, pp.381-398, 2015.

S. Lutsak, The Complexity of quasivariety lattices, Siberian Electronic Mathematical Reports, vol.14, pp.92-97, 2017.

L. Maksimova and &. V. Yun, Slices over minimal logic, Algebra i Logica, vol.55, issue.4, pp.449-464, 2016.
DOI : 10.1007/s10469-016-9399-0

T. Hosoi, On intermediate logics I, Journal of the Faculty of Science, vol.14, pp.293-312, 1967.

L. Maksimova and &. V. Yun, Strong decidability and strong recognizability, Algebra i Logica, vol.56, issue.5, 2017.
DOI : 10.1007/s10469-017-9459-0

S. V. Sudoplatov, Syntactic approach to constructions of generic models, Algebra and Logic, vol.46, issue.2, pp.134-146, 2007.

S. V. Sudoplatov, Classification of Countable Models of Complete Theories, 2018.

S. V. Sudoplatov, Generative classes generated by sets of diagrams, Novosibirsk State Technical University, vol.10, pp.163-174, 2015.

S. V. Sudoplatov, Classes of structures and their generic limits, Lobachevskii Journal of Mathematics, vol.36, pp.426-433, 2015.

Y. Kiouvrekis, P. &. Stefaneas, and . Sudoplatov, Definable sets in generic structures and their cardinalities, Siberian Advances in Mathematics, vol.28, pp.39-52, 2018.

V. Gould, Axiomatisability problems for S-systems, Journal of the London Mathematical Society, vol.2, issue.2, pp.193-201, 1987.

A. A. Stepanova, Axiomatizability and completeness of some classes of s-polygons, Algebra and Logic, vol.30, issue.5, pp.379-388, 1991.

A. A. Stepanova, Axiomatizability and model completeness of classes of regular polygons, Siberian Mathematical Journal, vol.35, issue.1, pp.181-193, 1994.

S. Bulman-fleming and &. V. Gould, Axiomatisability of weakly flat, flat and projective acts, Communications in Algebra, vol.30, issue.11, pp.5575-5593, 2002.

S. V. Sudoplatov, Syntactic approach to constructions of generic models, Algebra and Logic, vol.46, pp.134-146, 2007.

S. V. Sudoplatov, Classification of Countable Models of Complete Theories, 2018.

S. V. Sudoplatov, Generative classes generated by sets of diagrams, Algebra and Model Theory 10. Collection of papers, pp.163-174, 2015.

S. V. Sudoplatov, Classes of structures and their generic limits, Lobachevskii Journal of Mathematics, vol.36, pp.426-433, 2015.

Y. Kiouvrekis, P. Stefaneas, and S. V. Sudoplatov, Definable sets in generic structures and their cardinalities, Siberian Advances in Math, vol.28, pp.39-52, 2018.

S. S. Goncharov, 2005 Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '05, vol.12, pp.310-361, 2006.

A. H. Mekler, Stability of Nilpotent Groups of Class 2 and Prime Exponent, The Journal of Symbolic Logic, vol.46, issue.4, pp.781-788, 1981.

D. R. Hirschfeldt, B. Khoussainov, R. A. Shore-&-a, and . Slinko, Degree spectra and computable dimensions in algebraic structures, Annals of Pure and Applied Logic, vol.115, issue.1-3, pp.71-113, 2002.

D. A. Tussupov, Isomorphisms and Algorithmic Properties of Structures with Two Equivalences, Algebra and Logic, vol.55, issue.1, pp.50-57, 2016.

J. Johnson, J. F. Knight, V. Ocasio, J. Tussupov, and &. S. Vandendriessche, Preserving Categoricity and Complexity of Relations, Algebra and Logic, vol.54, issue.2, pp.140-154, 2015.

E. Fokina, A. Frolov, and &. Kalimullin, Categoricity Spectra for Rigid Structures, Notre Dame Journal of Formal Logic, vol.57, issue.1, pp.45-57, 2016.

S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, 1990.

T. G. Mustafin, On similarities of complete theories, Logic Colloquium '90: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, pp.259-265, 1990.

A. R. Yeshkeev-&-m and . Kassymetova, Jonsson theory and its classes of models, monograph, 2016.

A. R. Yeshkeev and M. T. Kassymetova, Jonsson theory and its classes of models, monograph, 2016.

B. Zilber, Zariski geometries: geometry from the logician's point of view, 2010.

C. Benzmüller and &. Paulson, Quantified multimodal logics in simple type theory, Logica Universalis, vol.7, issue.1, pp.7-20, 2013.

C. Benzmüller, L. Weber, and &. Paleo, Computer-assisted analysis of the Anderson-Hájek controversy, Logica Universalis, vol.11, issue.1, pp.139-151, 2017.

C. Benzmüller-&-b.-woltzenlogel and . Paleo, The inconsistency in Gödel's ontological argument: a success story for AI in metaphysics, IJCAI'16, Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, pp.936-942, 2016.

D. Davidson, Radical interpretation, Inquiries into Truth and Interpretation, p.125, 2001.

D. Fuenmayor and &. Benzmüller, Automating emendations of the ontological argument in intensional higher-order modal logic, KI * 2017: Advances in Artificial Intelligence, vol.10505, pp.114-127, 2017.

T. and K. Kissel, Logical Pluralism from a Pragmatic Perspective, Australasian Journal of Philosophy

M. Moortgat, Multimodal Linguistic Inference, Journal of Logic, Language and Information, vol.5, issue.3-4, pp.349-385, 1996.

M. Moortgat, Symmetric Categorial Grammar, Journal of Philosophical Logic, vol.38, issue.6, pp.681-710, 2009.
DOI : 10.1007/s10992-009-9118-6

M. Fitting, Possible world semantics for first order LP, Annals of Pure and Applied Logic, vol.165, pp.225-240, 2014.

K. Gödel and ;. S. Feferman, Unpublished essays and lectures, vol.III, 2001.

K. Gödel and ;. S. Feferman, On undecidable propositions of formal mathematical systems, Collected Works: Volume I: Publications 1929-1936, pp.1934-1964, 2001.

K. Gödel, Vortrag bei Zilsel, 1938.

K. Gödel, The modern development of the foundations of mathematics in the light of philosophy, 1961.

S. Kova?, Causal interpretation of Gödel's ontological proof, Gödel's ontological argument, 2015.

R. M. Burian, The Dilemma of Case Studies Resolved: The Virtues of Using Case Studies in the History and Philosophy of Science, Perspectives on Science, vol.9, issue.4, pp.383-404, 2001.

O. T. Hjortland, Anti-Exceptionalism about Logic, Philosophical Studies, vol.174, issue.3, pp.631-658, 2017.
DOI : 10.1007/s11098-016-0701-8

P. Mancosu, The Philosophy of Mathematical Practice, 2008.
URL : https://hal.archives-ouvertes.fr/halshs-00791899

G. Priest, Contradiction: A Study of the Transconsistent, 2006.

G. Priest, Revising logic, The Metaphysics of Logic, pp.211-223, 2014.
DOI : 10.1017/cbo9781139626279.016

T. Williamson, The Philosophy of Philosophy, Blackwell, 2007.

T. Williamson, Logic, Metalogic and Neutrality, Erkenntnis, vol.79, issue.2, pp.211-231, 2014.

R. Baillargeon, Object permanence in 3 1 2 -and 4 1 2 -months-old infants, Developmental Psychology, vol.23, issue.5, pp.655-664, 1987.

, Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898, 1992.

J. M. Mandler, The Foundations of Mind: Origins of Conceptual Thought, 2006.

C. S. Peirce, Training in Reasoning" (1898), in Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898, 1992.

E. Huntington, Sets of Independent Postulates for the Algebra of Logic, Transactions of the American Mathematical Society, vol.5, issue.3, pp.288-309, 1904.

A. Korselt, Bemerkung zur Algebra der Logik, Mathematische Annalen, vol.44, pp.156-157, 1894.

C. S. Peirce, On the algebra of logic, American Journal of Mathematics, vol.3, issue.1, pp.15-57

E. Schröder, VorlesungenüberVorlesungen¨Vorlesungenüber die Algebra der Logik, vol.1, p.1890

F. Bellucci-&-a-v.-pietarinen, Assertion and Denial: A Contribution from Logical Notation, Journal of Applied Logic, 2017.

C. S. Peirce, Manuscripts in the Houghton Library of Harvard University, identified by R. Robin, Annotated Catalogue of the Papers of Charles S. Peirce, Transactions of the Charles S, vol.7, pp.37-57, 1967.

M. Carrara, D. Chiffi, and &. Florio, Assertions and Hypotheses: A Logical Framework for their Opposition Relations, Logic Journal of the IGPL *, vol.25, issue.2, pp.131-144, 2017.

G. Boole, An Investigation of the Laws of Thought on which are founded the Mathematical Theories of Logic and Probabilities, p.1854

A. Morgan, Formal Logic: Or, the Calculus of Inference, Necessary and Probable, p.1847

C. Sanders-peirce, C. S. Writings-of, and . Peirce, A Chronological Edition, 7 volumes, 1982.

A. Tarski, Conferências na Unicamp em 1975 -Lectures at Unicamp in 1975, CLE * & Editora Unicamp „, 2016.

L. Borkowski, Autobiogram, Ruch Filozoficzny, vol.41, issue.1, pp.78-82, 1984.

L. Borkowski, Deductive Foundation and Analytic Propositions, Studia Logica, vol.19, issue.1, pp.59-74, 1966.

L. Borkowski, Dowód równowa? zno´scizno´sci dwóch sformuu lowa´nlowa´n klasycznej definicji prawdy, Roczniki Filozoficzne, vol.35, pp.87-99, 1987.

L. Borkowski-;-studia-logiczne, T. N. Kul-*, and L. , Kilka uwag o zasadzie dwuwarto´sciowo´scidwuwarto´sciowo´dwuwarto´sciowo´sci i logikach wielowarto´sciowychlowarto´sciowych, pp.469-475, 1990.

L. Borkowski, O definicji prawdy za pomoc a poj ecia stanu rzeczy opisywanego przez zdanie, Roczniki Filozoficzne, vol.41, issue.1, pp.23-25, 1993.

L. Borkowski, O matrycowych regu lach rachunku zda´nzda´n, pp.303-312, 1990.

L. Borkowski, O pewnym systemie logicznym opartym na reguu lach i jego zastosowaniu przy nauczaniu logiki matematycznej, pp.174-183, 1990.

L. Borkowski-;-studia-logiczne, T. N. Kul, and L. , O terminach modalnych, pp.138-173, 1990.

L. Borkowski, O twierdzeniu Gödla, Filozofia „, vol.7, pp.5-10, 1981.

L. Borkowski, Pewna wersja definicji klasycznego poj ecia prawdy, Roczniki Filozoficzne, vol.28, pp.119-131, 1980.

A. , Tratados de Lógica I y II (Organon), Biblioteca Clásica, Editorial Gredos, 2000.

J. Lukasiewicz, Selected Works, 1970.

P. D. Prieto, Indeterminación y Verdad. La polivalencia lógica en la Escuela de Lvov-Varsovia, 1995.

A. Garrido, Searching the arcane origins of Fuzzy Logic, BRAIN *, vol.2, issue.2, pp.51-57, 2011.

A. Garrido, , 2014.

A. Garrido and L. Aplicada, , 2014.

A. Garrido, Lógica Matemática e Inteligencia Artificial, 2015.

A. Garrido, , 2017.

S. C. Kleene, Introduction to Metamathematics, 1952.

S. Gottwald, A Treatise on Many-Valued Logics, 2001.

R. Murawski, Cracow Circle and Its Philosophy of Logic and Mathematics, Axiomathes, vol.25, issue.3, pp.359-376, 2015.

H. Rasiowa, An Algebraic Approach to Non-Classical Logics, 1974.

B. Smith, Austrian Philosophy: The Legacy of Brentano, 1994.

, The Vienna Circle and the Lvov-Warsaw School, Nijhoff International Philosophy Series, 1989.

J. Wole´nskiwole´nski and L. '-´-ecole-de-lvov-varsovie, Philosophie et Logique en Pologne (1895-1939), J. Vrin, 2012.

J. Wole´nskiwole´nski, Józef M. Boche´nskiBoche´nski and the Cracow Circle, vol.65, pp.5-15, 2013.

J. Wole´nskiwole´nski, Historico-Philosophical Essays, vol.1, 2013.

U. Wybraniec-skardowska, On Polish Logic from a historical perspective, 2009.

U. Wybraniec-skardowska, Zdzislaw Pawlak: Man, Creator and Innovator of Computer Science -Personal Memories, Proceedings of IJCRS „ , Part I, pp.3-12, 2017.

A. Zinoviev, Philosophical Problems of Many-Valued Logic, D. Reidel, 1963.

L. A. Zadeh, Fuzzy Sets, Information and Control, vol.8, issue.3, pp.338-353, 1965.

L. A. Zadeh, Fuzzy Logic and approximate reasoning, Synthese, vol.30, issue.3-4, pp.407-428, 1975.

, * Broad Research in Artificial Intelligence and Neuroscience „ International Joint Conference on Rough Sets

A. Grzegorczyk, Filozofia logiki i formalna logika niesymplifikacyjna" (Philosophy of Logic and Perceptive Equivalence), Zagadnienia Naukoznawstwa, vol.4, pp.445-450, 2011.

J. Goli´nskagoli´nska-pilarek and &. T. Huuskonen, Logic of descriptions. A new approach to the foundations of mathematics and science, Studies in Logic, Grammar and Rhetoric, vol.27, issue.40, pp.63-94, 2012.

J. Goli´nskagoli´nska-pilarek and &. T. Huuskonen, Grzegorczyk's non-Fregean logics and their formal properties, Applications of Formal Philosophy. The Road Less Traveled, vol.14, pp.243-263, 2017.

E. Lukasiewicz, P. Logiki-matematycznej, and . Wydawn, , 1929.

E. Marczewski, A general scheme of the notions of independence in mathematics, Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol.6, pp.731-736, 1958.

A. Tarski, Fundamentale Begriffe der Methodologie der deductiven Wissenshaften I, Montshefte für Mathematik und Physik, vol.37, pp.361-404, 1930.
DOI : 10.1007/bf01696782

K. Ajdukiewicz, O intencji pytania, Ruch Filozoficzny, vol.8, pp.152-153, 1923.

K. Ajdukiewicz, Zdanie pytajne, J ezyk i poznanie, vol.1, pp.278-286, 1960.

A. Bro?, Theory of Questions: Erotetics Through the Prism of Its Philosophical Background and Practical Applications, 2012.

T. Kubi´nskikubi´nski, Wst ep do logicznej teorii pyta´npyta´n, PWN, 1971.

T. Kubi´nskikubi´nski, An Outline of the Logical Theory of Questions, 1980.

D. Leszczy´nskaleszczy´nska-jasion, From Questions to Proofs. Beyond Logic of Questions and Proof Theory

P. Lupkowski, Logic of Questions in the Wild. Inferential Erotetic Logic in Information Seeking Dialogue Modelling, 2016.

A. Wi´sniewskiwi´sniewski, The Posing of Questions: Logical Foundations of Erotetic Inferences, 1995.

A. Wi´sniewskiwi´sniewski, Questions, Inferences, Scenarios, 2013.

K. Lewin, Der Begriff der Genese in Physik, 1992.

D. W. Zimmerman, Persistence and Presentism, Philosophical Papers, vol.25, issue.2, pp.115-126, 1996.

K. Ajdukiewicz, P. Ezyk-i-poznanie, and W. , , 1960.

M. Lechniak, Logika epistemiczna Jerzego Losia a teoria racjonalnego zachowania, Roczniki Filozoficzne, vol.36, pp.77-89, 1988.

M. Lechniak, Wielowarto´sciowo´s´cWielowarto´sciowo´Wielowarto´sciowo´s´Wielowarto´sciowo´s´c a poj ecia epistemiczne, Roczniki Filozoficzne, vol.54, issue.2, pp.375-390, 2006.

J. Lo´slo´s, Logiki wielowarto´sciowewielowarto´sciowe a formalizacja funkcji intensjonalnych, Kwartalnik Filozoficzny, vol.17, issue.1-2, pp.59-78, 1948.

J. Lo´slo´s, Podstawy analizy metodologicznej kanonów Milla, Annates Universitatis Mariae Curie-Shlodowska, Section F, vol.2, pp.269-301, 1948.

N. Rescher, Topics in Philosophical Logic, D. Reidel, 1968.

N. Rescher and &. Urquhart, Temporal Logic, 1971.

M. Tkaczyk, Logika temporalna, Metodologiczne i teoretyczne problemy kognitywistyki, 2014.

M. Tkaczyk, F. Contingentia, K. Wydawnictwo, and L. , , 2015.

M. Tkaczyk-&-t.-jarmu?-zek, N. Logiki-pozycyjne, K. Wydawnictwo, and L. , , 2015.

K. Twardowski, O tak zwanych prawdach wzgl ednych, Wybrane pisma filozoficzne, PWN, Warsaw, 1956. Abstraction principles via Le´sniewskianLe´sniewskian definitions: potential infinity and arithmetic

C. Rauszer, Representation theorem for semi-Boolean algebras I, Bulletin de l'Académie Polonaise des Scienses, vol.19, pp.881-887, 1971.

C. Rauszer, Semi-Boolean algebras and their applications to intuitionistic logic with dual operations, Fundamenta Mathematicae, vol.83, pp.81-87, 1974.

J. M. Boche´nskiboche´nski, Logic and Ontology, Philosophy East and West, vol.24, issue.3, pp.21-55, 1974.

A. Tarski, The Concept of Truth in Formalized Languages, Logic, Semantics, Metamathematics: Papers from 1923 to 1938, 1983.

J. C. Beall, Trivializing sentences and the promise of semantic completeness, Analysis, vol.75, issue.4, pp.573-584, 2015.

G. Priest, Old wine in (somewhat leaky) new bottles. Some comments on Beall, The Australasian Journal of Logic, vol.13, issue.5, 2016.

H. Barseghyan, The Laws of Scientific Change, 2015.

M. R. Martínez-ordaz, Holism, Inconsistency Toleration and Inconsistencies between Theory and Observation, Humana.Mente Journal of Philosophical Studies, vol.32, pp.117-147, 2017.

Z. Sebastien, The Status of Normative Propositions in the Theory of Scientific Change, Scientonomy, vol.1, pp.1-9, 2017.

J. Hansen, The Paradoxes of Deontic Logic: Alive and Kicking, Theoria, vol.72, issue.3, pp.221-232, 2006.

N. C. Da-costa, New Systems of Predicate Deontic Logic, The Journal of Non-Classical Logic, vol.5, pp.75-80, 1988.

M. Clark, Paradoxes from A to Z, 2012.

P. Eldridge-smith, Paradoxes and Hypodoxes of Time Travel, Art and Time, pp.172-189, 2007.

P. Eldridge-smith, The Liar Paradox and its Relatives, 2008.

P. Eldridge-smith, A Hypodox! A Hypodox! A Disingenuous Hypodox!, The Reasoner, vol.6, issue.7, pp.118-119, 2012.

P. Eldridge-smith, Two Paradoxes of Satisfaction, vol.124, pp.85-119, 2015.

J. L. Mackie, Truth, Probability and Paradox: Studies in Philosophical Logic, 1973.

R. Sorensen, A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind, 2003.

R. T. Cook, A Dictionary of Philosophical Logic, 2009.

M. Detlefsen, D. C. Mccarty, and &. B. Bacon, Logic from A to Z, 1999.

H. Field, Is the Liar Sentence Both True and False?, Deflationism and Paradox, pp.23-40, 2005.

S. Haack, Philosophy of Logics, 1978.

H. Price, Why 'Not' ?, Mind, vol.99, issue.394, pp.221-238, 1990.

H. Slater, Paraconsistent Logics?, Journal of Philosophical Logic, vol.24, issue.4, pp.451-454, 1995.

P. Besnard and &. Wong, Modal (Logic) Paraconsistency, European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, vol.2711, pp.540-551, 2003.

J. Béziau, Paraconsistent logic from a modal viewpoint, Journal of Applied Logic, vol.3, issue.1, pp.7-14, 2005.

J. Bueno-soler, Two semantical approaches to paraconsistent modalities, Logica Universalis, vol.4, issue.1, pp.137-160, 2010.

D. A. Costa-&-m and . Martins, Paraconsistency in hybrid logic, Journal of Logic and Computation, vol.27, issue.6, pp.1825-1852, 2017.

D. Harel, J. Tiuryn-&-d.-kozen, and D. Logic, , 2000.

A. Madeira, R. &. Neves, and . Martins, An exercise on the generation of many-valued dynamic logics, Journal of Logical and Algebraic Methods in Programming, vol.85, issue.5, pp.1011-1037, 2016.

J. Marcos, Modality and Paraconsistency, pp.213-222, 2004.

U. Rivieccio, A. Jung, and &. Jansana, Four-valued modal logic: Kripke semantics and duality, Journal of Logic and Computation, vol.27, issue.1, pp.155-199, 2017.

I. Sedlár, Propositional Dynamic Logic with Belnapian Truth Values, Advances in Modal Logic, vol.11, pp.503-519, 2016.

, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, * Massachusetts Institute of Technology References 1. J. Lukasiewicz, 1957.

T. Skura-&-r and . Tuziak, Three-valued Maximal Paraconsistent Logics, Logika, vol.23, 2005.

O. Arieli, A. Avron, and &. Zamansky, Maximally Paraconsistent ThreeValued Logics, Twelfth International Conference on the Principles of Knowledge Representation and Reasoning, 2010.

S. Ja´skowskija´skowski, A propositional Calculus for Inconsistent Deductive Systems, Studia Societatis Scientiarum Torunensis, vol.1, pp.35-56, 1948.

M. Urchs, Just Complexity, New Directions in the Philosophy of Science, pp.203-219, 2014.

F. Kroon, Realism and Dialetheism, The Law of Non-Contradiction: New Philosophical Essays, pp.245-263, 2004.

T. E. Tahko, The Law of Non-Contradiction as a Metaphysical Principle, Australasian Journal of Logic, vol.7, pp.32-47, 2009.

G. Priest, Contradiction: A Study of the Transconsistent, 2006.

D. V. Lindley, The Philosophy of Statistics, Journal of the Royal Statistical Society. Series D (The Statistician), vol.49, issue.3, pp.293-337, 2000.

D. V. Lindley, O. Interview-by-tony, and . Hagan, Bayes 250 Conference * , Royal Statistical Society, 2013.

D. W. Miller-&-k and . Popper, A proof of the impossibility of inductive probability, Nature, vol.302, pp.687-688, 1983.

D. W. Miller-&-k and . Popper, Deductive Dependence, Actes IV CongrèsCataì a de Lógica, pp.21-29, 1986.

D. W. Miller, . R. „k, and . Popper, Deductive Dependence", digitally remastered version from, 1989.

K. R. Popper, The Non-existence of Probabilistic Inductive Support, Foundations of Logic and Linguistics, pp.303-318, 1985.

P. Roeper and &. Leblanc, Probability Theory and Probability Logic, 1999.

W. A. Carnielli, M. E. Coniglio, and &. J. Marcos, Logics of Formal Inconsistency, Handbook of Philosophical Logic, 2007.

D. W. Miller, Popper's contributions to the theory of probability and its interpretation", in The Cambridge Companion to Popper, pp.230-268, 2016.

K. R. Popper, The Logic of Scientific Discovery, 1959.

J. Bueno-soler and &. W. Carnielli, Paraconsistent Probabilities: Consistency, Contradictions and Bayes' Theorem, vol.18, 2016.

W. A. Carnielli-&-m and . Coniglio, of Logic, Epistemology, and the Unity of Science book series, Paraconsistent Logic: Consistency, Contradiction and Negation, vol.40, 2016.

K. R. Popper, A Note on Probability, The Logic of Scientific Discovery, vol.47, pp.318-322, 1938.

R. Blanché, Essai sur l'Organisation Systé-matique des Concepts, J. Vrin, 1966.

W. Borges and J. M. Stern, The Rules of Logic Composition for the Bayesian Epistemic e-values, Logic Journal of the IGPL *, vol.15, pp.401-420, 2007.

L. G. Esteves, R. Izbicki, J. M. Stern-&-r, and . Stern, The Logical Consistency of Simultaneous Agnostic Hypothesis Tests, Entropy Journal, vol.18, issue.7, 2016.

R. G. Izbicki-&-l and . Esteves, Logical Consistency in Simultaneous Statistical Test Procedures, Logic Journal of IGPL, vol.23, issue.5, pp.732-758, 2015.

C. A. Pereira and &. M. Stern, Evidence and Credibility: Full Bayesian Signicance Test for Precise Hypotheses, Entropy Journal, vol.1, issue.4, pp.99-110, 1999.

J. M. Stern, R. Izbicki, L. G. Esteves-&-r, and . Stern, LogicallyConsistent Hypothesis Testing and the Hexagon of Oppositions, Logic Journal of IGPL, vol.25, issue.5, pp.741-757, 2017.

J. M. Stern, Paraconsistent Sensitivity Analysis for Bayesian Significance Tests, Brazilian Symposium on Artificial Intelligence, vol.3171, pp.134-143, 2004.

G. Shafer and &. Vovk, The Sources of Kolmogorov's Grundbegriffe, Statistical Science, vol.21, issue.1, pp.70-98, 2006.

Y. I. Alimov, English version in Studies in the History of, An Alternative to the Method of Mathematical Statistics, vol.2, pp.122-133, 1980.

N. Cartwright, The Dappled World: A Study of the Boundaries of Science, p.320, 1999.

W. A. Carnielli and &. Rodrigues, An epistemic approach to paraconsistency: a logic of evidence and truth, Synthese, 2017.

. References, Links and Suggested Readings

S. Al-fedaghi, Context-aware software systems: Toward a diagrammatic modeling foundation, Journal of Theoretical and Applied Information Technology, vol.95, issue.4, pp.936-947, 2017.

J. Barwise and &. Etchemendy, Language, Proof and Logic, 1999.

E. F. Codd, A relational model of data for large shared data banks, Communications of the ACM *, vol.13, issue.6, pp.377-387, 1970.

E. F. Codd, The Relational Model for Database Management: Version 2, 1990.

M. Collins, Head-driven Statistical Models for Natural Language Parsing, 1999.

W. Croft, Syntactic Categories and Grammatical Relations: The Cognitive Organization of Information, 1991.

C. J. Date, An Introduction to Database Systems, 2003.

C. J. Date and &. Darwen, Foundation for Future Database Systems: The Third Manifesto, 2000.

P. Domingos, S. Kok, H. Poon, M. Richardson, and &. Singla, Unifying logical and statistical AI, AAAI'06 * Proceedings of the 21st National Conference on Artificial Intelligence, vol.1, pp.2-7, 2006.

T. Kwiatkowski, E. Choi, Y. Artzi, and &. Zettlemoyer, Scaling semantic parsers with on-the-fly ontology matching, Proceedings of 2013 Conference on EMNLP „, pp.1545-1556, 2013.

L. Libkin, Incomplete data: what went wrong, and how to fix it, PODS'14 Proceedings of the 33rd ACM § SIGMOD ¶ -SIGACT † -SIGART ** Symposium on Principles of Database Systems, Association for Computing Machinery, pp.1-13, 2014.

J. Lukasiewicz, Philosophical remarks on many-valued systems of propositional logic, Selected Works by Jan Lukasiewicz, 1930.

W. Mallede, F. Marir, and &. Vassiles, Algorithms for mapping RDB schema to RDF for facilitating access to deep web, Proceedings of WEB 2013: The First International Conference on Building and Exploring Web Based Environments, pp.32-41, 2013.

D. Mcgoveran, Nothing from Nothing, Relational Database Writings, 1994.

S. Russell and &. Norvig, Artificial Intelligence: A Modern Approach, 2003.

S. Shavel and &. E. Thomsen, A Tractarian Approach to Information Modeling, Wittgenstein Toward a Re-Evaluation: Proceedings of the 14th International Witgenstein-Symposium Centenary Celebration, 1992.

J. Samuel and &. Rey, DaWeS: Data Warehouse fed with Web Services, Actes du XXXIIème Congrès INFORSID *, pp.329-344, 2014.

J. Samuel and &. Rey, Integration of Multiple Heterogeneous and Autonomous Web Services using Mediation Approach: Open Challenges, Journal on Advances in Theoretical and Applied Informatics, vol.2, issue.2, pp.38-46, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01421210

A. Cussins, Subjectivity, Objectivity and Frames of References in Evan's Theory of Thought, Electronic Journal for Analytic Philosophy, 1999.

N. Eilan, R. Mccarthy, and &. B. Brewer, Spatial Representation: Problems in Philosophy and Psychology, 1999.

G. Evans, Varieties of Reference, 1982.

G. Evans, Collected Papers, 1996.

G. Frege, The Thought: A Logical Inquiry, Mind, New Series, vol.65, pp.289-311, 1956.

M. Luntley, Dynamic Thoughts and Empty Minds, European Review of Philosophy, vol.2, pp.77-103, 1997.

H. Poincaré, The value of science, 1905.

P. F. Strawson, Individuals: An essay in descriptive metaphysics, 1991.

C. Pshenichny, Qualitative and quantitative calculi in the theory of multitudes, Dynamic Knowledge Representation in Scientific Domains, 2018.

C. A. Pshenichny, S. I. Nikolenko, R. Carniel, P. A. Vaganov, Z. V. Khrabrykh et al., The event bush as a semantic-based numerical approach to natural hazard assessment (exemplified by volcanology), Computers and Geosciences, vol.35, issue.5, pp.1017-1034, 2009.

C. A. Pshenichny-&-o and . Kanzheleva, Theoretical foundations of the event bush method, GSA „ Special Papers, vol.482, pp.139-164, 2011.

U. Wolter, Scenarios in event bushes -a formal proposal, Dynamic Knowledge Representation in Scientific Domains, 2018.

P. Diviacco, C. Pshenichny, R. Carniel, Z. Khrabrykh, V. Shterkhun et al., Organization of a geophysical information space by using an event-bush-based collaborative tool, Earth Science Informatics, vol.8, issue.3, pp.677-695, 2015.

C. J. Ducasse-&-h and . Curry, Early History of the Association for Symbolic Logic, The Journal of Symbolic Logic, vol.27, issue.3, pp.255-258, 1962.

, The arbitrariness of the sign in question, 2018.

P. Halmos, How to write mathematics, L'enseignement mathématique, vol.16, issue.2, pp.123-152, 1970.

J. Venn, Symbolic Logic, p.1881

A. Tarski, Contributions to the theory of models. I, II, III, Indigationes Mathematicae, vol.16, pp.56-64, 1954.

M. E. Barth-&-e and . Krabbe, From Axiom to Dialogue: A Philosophical Study of Logics and Argumentation, 1982.

A. , Logic and theory of representation, Logic in question -7

A. , La Fondation analogique des représentations, 2005.

A. Bacon, Non-classical Metatheory for Non-classical Logics, Journal of Philosophical Logic, vol.42, issue.2, pp.335-355, 2013.

M. K. Chakraborty, Graded consequence: further studies, Journal of Applied Non-Classical Logics, vol.5, issue.2, pp.227-238, 1995.

M. K. Chakraborty and &. S. Basu, Graded Consequence and Some Metalogical Notions Generalized, Fundamenta Informaticae, vol.32, issue.3-4, pp.299-311, 1997.

M. K. Chakraborty and &. S. Dutta, Graded consequence revisited, Fuzzy Sets and Systems, vol.161, issue.14, pp.1885-1905, 2010.

S. K. Dutta-&-m and . Chakraborty, The role of metalanguage in graded logical approaches, Fuzzy Sets and Systems, vol.298, pp.238-250, 2016.

G. Malinowski, Q-consequence operation, Reports on Mathematical Logic, vol.24, pp.49-59, 1990.

G. Malinowski, Inferential Many-Valuedness, Philosophical Logic in Poland, pp.75-84, 1994.

H. Marraud, Razonamiento Approximado y Grados De Consecuencia, vol.10, pp.55-70, 1998.

D. P. Muino, A Graded Inference Approach Based on Infinite-Valued Lukasiewicz Semantics, Proceedings of The International Symposium on Multiple-Valued Logic, pp.252-257, 2010.

D. P. Muino, A Consequence Relation for Graded Inference within the Frame of Infinite-valued Lukasiewicz Logic, Fundamenta Informaticae, vol.123, issue.1, pp.77-95, 2013.

R. Parikh, The Problem of Vague Predicates, Language, Logic and Method, pp.241-261, 1983.

C. Pelta, Wide sets, deep many-valuedness and sorites arguments, Mathware & Soft Computing, vol.11, issue.1, pp.5-11, 2004.

Y. She, On the rough consistency measures of logic theories and approximate reasoning in rough logic, International Journal of Approximate Reasoning, vol.55, issue.1, pp.486-499, 2014.

T. Vetterlein, F. Esteva, and &. Godo, Logics for Approximate Entailment in ordered universes of discourse, International Journal of Approximate Reasoning, vol.71, pp.50-63, 2016.

, Call for papers Relevant topics include

I. Hacking, Why is There Philosophy of Mathematics at All, 2014.

L. Wittgenstein, Philosophical Investigations, 1953.

L. Wittgenstein, Remarks on the Foundations of Mathematics, 1956.

L. Wittgenstein, Lectures on the Foundations of Mathematics, 1939.

J. Conant, The search for logically alien thought: Descartes, Kant, Frege, and the Tractatus, Philosophical Topics, vol.20, issue.1, pp.115-180, 1992.

C. Diamond, Criticising from "Outside, Philosophical Investigations, vol.36, pp.114-132, 2013.

C. Diamond, How Old Are These Bones? Wittgenstein, Putnam and Verification, Proceedings of the Aristotelian Society, Supplementary Volumes, vol.73, pp.99-150, 1999.

C. Diamond, Putnam and Wittgensteinian Baby-Throwing: Variations on a Theme, The Philosophy of Hilary Putnam, pp.603-639, 2015.

C. Diamond, The Skies of Dante and Our Skies: A Response to Ilham Dilman, Philosophical Investigations, vol.35, pp.187-204, 2012.

C. Diamond, Truth: Defenders, Debunkers, Despisers, Commitment in Reflection: Essays in Literature and Moral Philosophy, pp.195-222, 1994.

I. Dilman, Wittgenstein's Copernican Revolution: The Question of Linguistic Idealism, 2002.

E. E. Evans-pritchard, Witchcraft, Oracles and Magic among the Azande, 1937.

P. Winch, The Idea of a Social Science and Its Relation to Philosophy, 1958.

P. Winch, Understanding a Primitive Society, American Philosophical Quarterly, vol.1, issue.4, pp.307-324, 1964.

L. Wittgenstein, Tractatus Logico-Philosophicus, 1974.

G. W. Hegel, Werke in zwanzig Bänden. Theorie Werkausgabe, new edition on basis of the works of 1832-1845, 1969.

G. W. Hegel, Hegel's Science of Logic, English translation by A. Miller, Humanity Books, 1969.

G. W. Hegel, The Encyclopaedia Logic, Part I of Encyclopaedia of Philosophical Sciences with Additions, 1991.

G. W. Hegel, VorlesungenüberVorlesungen¨Vorlesungenüber Logik und Metaphysik, 1992.

A. Lewis, Paranoia and paranoid: a historical perspective, Psychological Medicine, vol.1, issue.1, pp.2-12, 1970.

A. Fried and &. Agassi, Paranoia: A Study in Diagnosis, 1976.

. *-"ff,

I. M. Blanco, The Unconscious as Infinite Sets: An Essay in Bi-logic, 1975.

C. Ginzburg, Ecstasies: Deciphering the Witches' Sabbath, 1989.

F. Orlando, lettura del "Gattopardo, 1998.

J. Coulter, Logic: Ethnomethodology and the Logic of Language, Ethnomethodology and the Human Sciences, pp.20-50, 1991.

J. Coulter, Chance, cause and conduct: probability theory and the explanation of human action, Philosophy of Science, Logic and Mathematics in the Twentieth Century, vol.9, pp.266-291, 1996.

H. Dreyfus, What Computers Still Can't Do: A Critique of Artificial Reason, revised edition, 1992.

H. Dreyfus, &. C. Taylor, and R. Realism, , 2015.

N. J. Enfield and &. Sidnell, On the concept of action in the study of interaction, Discourse Studies, vol.19, issue.5, pp.515-535, 2017.

C. Greiffenhagen and &. Sharrock, Logical Relativism: Logic, Grammar, and Arithmetic in Cultural Comparison, Configurations, vol.14, issue.3, pp.275-301, 2008.

G. Kohs, A. , and M. Pictures, , 2017.

E. Livingston, Ethnomethodological Studies of Mediated Interaction and Mundane Expertise, The Sociological Review, vol.54, issue.3, pp.405-425, 2006.

. Ph and . Sormani, Fun in Go: The Timely Delivery of a Monkey Jump and Its Lingering Relevance to Science Studies, Human Studies, vol.38, issue.2, pp.281-308, 2015.

. Ph and . Sormani, Power in Go: Material Practice, a Perspicuous Setting, and Its Praxeological Implications", in Ethnomethodology and Conversation Analysis, session of, Annual Meeting, 2017.

. Ph and . Sormani, Power in Go: Instructional Matter, Algorithmic Drama, and Symmetry Politics

K. S. Donnellan, Reference and Definite Descriptions, The Philosophical Review, vol.75, issue.3, pp.281-304, 1966.

K. S. Donnellan, The contingent a priori and rigid designators, Midwest Studies in Philosophy, vol.2, pp.12-27, 1977.

M. Dummet, Frege: Philosophy of Language, 1973.

J. Hintikka, Modality as Referential Multiplicity, Ajatus, vol.20, pp.49-64, 1957.

J. Hintikka, Knowledge and Belief, 1962.

J. Hintikka and &. Sandu, The Fallacies of the New Theory of Reference, Synthese, vol.104, issue.2, pp.245-283, 1995.

S. Kripke, Naming and Necessity, 1980.

T. Tulenheimo, Objects and Modalities -A Study in the Semantics of Modal Logic, 2017.

R. L. Epstein, Relatedness and Implication, Philosophical Studies, vol.36, issue.2, pp.137-173, 1979.

R. L. Epstein, The Semantic Foundations of Logic, vol.1, 1990.

J. Hintikka, Knowledge and Belief: An Introduction to the Logic of the Two Notions, 1962.

T. Jarmu? and &. B. Kaczkowski, On some Logic with a Relation Imposed on Formulae: Tableau System F, Bulletin of the Section of Logic, vol.43, issue.1-2, pp.53-72, 2014.

J. Hintikka, What was Aristotle Doing in His Early Logic, Anyway? A Reply to Woods and Hansen, vol.113, pp.241-249, 1997.

A. and P. Analytics, , 1989.

J. Hintikka, Kant on Existence, Predication, and the Ontological Argument, Dialectica, vol.35, issue.1-2, pp.127-146, 1981.

M. Jamnik, Mathematical Reasoning with Diagrams: From Intuition to Automation, Center for the Study of Language and Information, 2002.

R. Krömer, Tool and Object: A History and Philosophy of Category Theory, Birkhäuser, 2007.

M. Lipman, Thinking in Education, 2003.

D. Moshman, From inference to reasoning: the construction of rationality, Thinking and Reasoning, vol.10, pp.221-239, 2004.

R. Pears and &. P. Bryant, Transitive inferences by young children about spatial position, British Journal of Psychology, vol.81, issue.4, pp.497-510, 1990.

J. Piaget, Part I: Cognitive Development in Children: Piaget Development and Learning, vol.2, pp.176-186, 1964.

M. Sasseville and &. Gagnon, Penser ensemblè a l'´ ecole: Des outils pour l'observation d'une communauté de recherche philosophique en action, 2012.

P. C. Wason, Regression in reasoning?, British Journal of Psychology, vol.60, issue.4, pp.471-480, 1969.

K. Augutis, Effective use of a computer at school" (in Lithuanian, Contest entry, 1997.

A. Kulikauskas and &. S. Maskeliunas, Organizing Thoughts into Sequences, Hierarchies and Networks, 4th International Workshop on Evaluation of Modeling Methods in Systems Analysis and Design, 1999.

J. Bénabou, Introduction to Bicategories, Reports of the Midwest Category Seminar, vol.47, pp.1-77, 1967.

G. M. Kelly-&-r and . Street, Review of the elements of 2-categories, Category Seminar, vol.420, pp.75-103, 1974.

F. L. Nunes, Freely generated n-categories, coinserters and presentations of low dimensional categories, 2017.

A. J. Power, A 2-categorical pasting theorem, Journal of Algebra, vol.129, issue.2, pp.439-445, 1990.

D. Blackwell, Basic Statistics, 1969.

M. H. Degroot, Optimal Statistical Decisions, 2004.

D. V. Lindley, Making Decisions, 1985.

J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988.

M. Acclavio, Proof diagrams for multiplicative linear logic: Syntax and semantics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01931400

J. C. Baez and &. Lauda, A prehistory of n-categorical physics, 2009.

A. Burroni, Higher-dimensional word problems with applications to equational logic, Theoretical Computer Science, vol.115, issue.1, pp.43-62, 1993.

G. Gentzen, Investigations into Logical Deduction, The collected papers of Gerhard Gentzen, 1969.

P. Selinger, A Survey of Graphical Languages for Monoidal Categories, New Structures for Physics, pp.289-355, 2010.

P. Arndt, R. Jansana, H. L. Mariano-&-d, and . Pinto, Filter functors in logic and applications to categorial analysis of meta-logic properties, 2016.

W. J. Blok, &. Pigozzi, and A. Logics, Memoirs of the American Mathematical Society, vol.77, issue.396, 1989.

A. Brunner, H. L. Mariano-&-s, and . Da-silva, Categorial forms of the axiom of choice, Logic Journal of the IGPL *, vol.25, issue.4, pp.408-430, 2017.

M. Kashiwara and &. Schapira, Categories and Sheaves, 2006.

C. Domínguez and &. Duval, Diagrammatic logic applied to a parameterisation process, Mathematical Structures in Computer Science, vol.20, issue.4, pp.639-654, 2010.

C. Domínguez and &. Duval, A parameterization process: from a functorial point of view, International Journal of Foundations of Computer Science, vol.23, issue.1, pp.225-242, 2012.

D. Duval, Diagrammatic Specifications, Mathematical Structures in Computer Science, vol.13, issue.6, pp.857-890, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00171562

D. Duval, Diagrammatic inference, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00177075

P. Gabriel-&-m.-zisman, Ergebnisse der Mathematik und ihrer Grenzgebiete book series, Calculus of Fractions and Homotopy Theory, vol.35, 1967.

P. Johnstone, Fibrations and partial products in a 2-category, Applied Categorical Structures, vol.1, issue.2, pp.141-179, 1993.

R. Street, Fibrations and Yoneda's lemma in a 2-category, Proceedings of Sydney Category Theory Seminar, vol.420, pp.104-133, 1972.

S. Vickers, Sketches for arithmetic universes, 2016.

W. J. Blok and &. Pigozzi, Algebraizable Logics, Memoirs of the American Mathematical Society book series, vol.77, 1989.

H. L. Mariano-&-c and . Mendes, Towards a good notion of categories of logics, 2014.

D. C. Pinto-&-h and . Mariano, Algebraizable logics and a functorial encoding of its morphisms, Logic Journal of the IGPL *, vol.25, issue.4, pp.524-561, 2017.

G. Voutsadakis, On the Categorical Algebras of First-Order Logic, Scientiae Mathematicae Japonicae Online, vol.10, pp.47-54, 2004.

P. Arndt, Homotopical categories of logics, The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol.1, pp.13-58, 2015.

C. Caleiro-&-r and . Gonçalves, Equipollent logical systems, Logica Universalis: Towards a General Theory of Logic, pp.97-109, 2007.

W. Carnielli, M. Coniglio, D. M. Gabbay, P. Gouveia, and &. Sernadas, Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems, 2008.

C. Mendes and H. L. Mariano, Towards a good notion of categories of logics, 2016.

P. S. Terraf-&-d and . Vaggione, Varieties with definable factor congruences, Transactions of the American Mathematical Society, vol.361, issue.10, pp.5061-5088, 2009.

W. Zuluaga, Representación por haces de riRigs, 2016.

F. W. Lawvere, Core varieties, extensivity, and rig geometry, Theory and Applications of Categories, vol.20, issue.14, pp.497-503, 2008.

C. Fouqueré and &. Quatrini, Un cadre formel issu de de la théorie de la démonstration pour la théorie de l'argumentation, Mathématiques et Sciences Humaines, vol.198, issue.2, pp.49-83, 2012.

J. Girard, Locus solum: From the rules of logic to the logic of rules, Mathematical Structures in Computer Science, vol.11, issue.3, pp.301-506, 2001.

J. Adam and . Linguística, Introduçãò a Análise Textual dos Discursos, 2011.

, ¯ ul al-Fiqh li'l-Shaykh Ab¯ ? Ish . ¯ aq Ibr¯ ah ¯ im b 'Al¯ ? b Y¯ usuf al-Sh¯ ?r¯ az¯ ?, vol.2, 1407.

W. E. Young, The Dialectical Forge: Juridical Disputation and the Evolution of Islamic Law, 2017.

P. Bartha, By Parallel Reasoning, 2010.

S. Brewer, Exemplary Reasoning: Semantics, Pragmatics, and the Rational Force of Legal Argument by Analogy, Harvard Law Review, vol.109, issue.5, pp.923-1028, 1996.

S. Rahman and &. Iqbal, Epistemic and Dialectical Meaning within Ab¯ u Ish . ¯ aq al-Sh¯ ?r¯ az¯ ?'s System of Co-Relational Inferences of the Occasioning Factor, 2016.

P. Cintula, C. G. Fermüller, and &. Noguera, Fuzzy Logic, The Stanford Encyclopedia of Philosophy, 2016.

D. Edgington, The Philosophical Problem of Vagueness, Legal Theory, vol.7, issue.4, pp.371-378, 2001.

T. Endicott, Law is Necessarily Vague, Legal Theory, vol.7, issue.4, pp.379-385, 2001.

T. Endicott, The Value of Vagueness, Philosophical Foundations of Language in the Law, pp.14-30, 2011.

D. Graff, Shifting sands: an interest-relative theory of vagueness, Philosophical Topics, vol.28, issue.1, pp.45-81, 2000.

S. Halldén, The Logic of Nonsense

B. F. Chellas, Modal Logic: An Introduction, 1980.

H. Herrestad and &. Krogh, Obligations directed from bearers to counterparties, Proceedings of the International Conference on Artificial Intelligence and Law, pp.210-218, 1995.

W. N. Hohfeld, Fundamental legal conceptions applied in judicial reasoning, Fundamental Legal Conceptions Applied in Judicial Reasoning and Other Legal Essays, pp.23-64, 1923.

S. Kanger, New foundations of ethical theory, Deontic Logic: Introductory and Systematic Readings, pp.36-58, 1971.

S. Kanger, Law and logic, Theoria, vol.38, issue.3, pp.105-132, 1972.

S. Kanger, On realization of human rights, Acta Philosophica Fennica, vol.38, 1985.

L. , Stig Kanger's Theory of Rights, Logic, Methodology and Philosophy of Science IX, pp.889-911, 1994.

D. Makinson, On the formal representation of rights relations: Remarks on the work of Stig Kanger and Lars Lindahl, Journal of Philosophical Logic, vol.15, issue.4, pp.403-425, 1986.

C. Wellman, Relative duties in the law, Philosophical Topics, vol.18, issue.1, pp.183-202, 1990.

B. P. Bolzano, . Wissenschaftslehre, . Seidel'sche, . Buchhandlung, and . Sulzbach-rosenberg, English translation: Theory of Science, vol.1837, 2014.

L. J. Cohen, The Probable and the Provable, 1977.

A. P. Dawid, The Difficulty About Conjunction, Journal of the Royal Statistical Society, Series D (The Statistician), vol.36, issue.2-3, pp.91-97, 1987.

A. N. Kolmogorov, English translation: Foundations of the Theory of Probability, Grundbegriffe der Wahrscheinlichkeitsrechnung, 1933.

D. A. Schum, A Review of a Case against Blaise Pascal and His Heirs, Michigan Law Review, vol.77, issue.3, pp.446-483, 1979.

R. Dworkin, Taking Rights Seriously, 1977.

S. Soames, Interpreting Legal Texts: What Is, and What Is Not, Special about the Law, Philosophical Essays, vol.1, 2009.

R. Sorensen, How Vagueness Makes Judges Lie, Vagueness in the Law: Philosophical and Legal Perspectives, pp.297-316, 2016.

R. J. Allen, No Plausible Alternative to a Plausible Story of Guilt as the Rule of Decision in Criminal Cases, Proof and Standards of Proof in the Law, pp.10-27, 2010.

E. K. Cheng, Reconceptualizing the Burden of Proof, The Yale Law Journal, vol.122, issue.5, pp.1104-1371, 2013.

L. J. Cohen, The Probable and the Provable, 1977.

L. J. Cohen, Subjective probability and the paradox of the gatecrasher, Arizona State Law Journal, vol.2, issue.2, pp.627-634, 1981.

A. P. Dawid, The Difficulty About Conjunction, Special Issue: Practical Bayesian Statistics, vol.36, pp.91-97, 1987.

J. Earman, Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory, 1992.

S. Haack, Evidence Matters: Science, Proof, and Truth in the Law, 2014.

S. Haack, Legal Probabilism: An Epistemological Dissent, pp.47-77, 2014.

C. R. Nesson, Reasonable doubt and permissive inferences: The value of complexity, Harvard Law Review, vol.92, issue.6, pp.1187-1225, 1979.

L. H. Tribe, The Continuing Debate over Mathematics in the Law of Evidence: A Further Critique of Mathematical Proof, Harvard Law Review, vol.84, issue.8, pp.1810-1820, 1971.

L. H. Tribe, Trial by mathematics: Precision and ritual in the legal process, Harvard Law Review, vol.84, issue.6, pp.1329-1393, 1971.

B. D. Underwood, The thumb on the scale of justice: Burdens of persuasion in criminal cases, Yale Law Journal, vol.86, issue.7, pp.1299-1348, 1977.

S. Ja´skowskija´skowski, A Propositional Calculus for Inconsistent Deductive Systems, Studia Societatis Scientiarum Torunensis, vol.1, pp.35-56, 1948.

J. Lukasiewicz, On Aristotle's principle of contradiction, PWN *, 1987.

B. Coecke and &. Kissinger, Picturing Quantum Processes. A first course on quantum theory and diagrammatic reasoning, 2017.

B. Coecke, M. Sadrzadeh, and &. S. Clark, Mathematical Foundations for a Compositional Distributional Model of Meaning, A Festschrift for Jim Lambek, vol.36, pp.345-384, 2010.

J. Bolt, B. Coecke, F. Genovese, M. Lewis, D. Marsden et al., Interacting Conceptual Spaces I : Grammatical Composition of Concepts, 2017.

G. Boole, The Mathematical Analysis of Logic. Being an Essay To a Calculus of Deductive Reasoning, p.1847

F. Dubois and &. Toffano, Eigenlogic: a Quantum View for MultipleValued and Fuzzy Systems, International Symposium on Quantum Interaction, QI 2016, vol.10106, pp.239-251, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01464903

Z. Toffano, Eigenlogic in the spirit of George Boole, pp.2015-2018

Z. Toffano and &. Dubois, Interpolating Binary and Multivalued Logical Quantum Gates, The 4th International Electronic Conference on Entropy and Its Applications, vol.2, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01639802

S. Abramsky and &. Coecke, A categorical semantics of quantum protocols, Proceedings of the 19th Annual IEEE * Symposium on Logic in Computer Science, LICS „ '04, pp.415-425, 2004.

G. Chiribella, G. M. D'ariano, and &. P. Perinotti, Informational derivation of quantum theory, Physical Review A, vol.84, issue.1, 2011.

B. Coecke-&-r and . Lal, Categorical quantum mechanics meets the pavia principles: towards a representation theorem for cqm constructions, Quantum Physics and Logic, hold in, p.67, 2011.

B. O. Coecke-&-´-e and . Paquette, Categories for the Practising Physicist, New Structures for Physics, vol.813, pp.173-286, 2010.

L. Hardy, Quantum Theory From Five Reasonable Axioms, 2001.

L. Hardy, Reformulating and Reconstructing Quantum Theory, 2011.

C. Heunen and &. Jacobs, Quantum logic in dagger kernel categories, Order, vol.27, issue.2, pp.177-212, 2010.

M. P. Soì-er, Characterization of Hilbert spaces by orthomodular spaces, Communications in Algebra, vol.23, issue.1, pp.219-243, 1995.

J. Neumann, Mathematical Foundations of Quantum Mechanics, 1955.

A. Wilce, A Royal Road to Quantum Theory (or Thereabouts)", extended abstract, Proceedings of 13th International Conference on Quantum Physics and Logic, 2016.

J. C. Beall and &. Restall, Logical Pluralism, 2006.

R. B. Brandom, Making it Explicit: Reasoning, Representing, and Discursive Commitment, 1994.

J. Peregrin, Inferentialism: Why Rules Matter, 2014.

, New Directions in Paraconsistent Logic: Proceedings of the 5th World Congress on Paraconsistency, 2014.

B. Brown, Symmetrical Preservation Relations and Cognitive Commitments

P. Raatikainen, On rules of inference and the meanings of logical constants, Analysis, vol.68, issue.300, pp.282-287, 2008.

J. Barwise, Axioms for abstract model theory, Annals of Logic, vol.7, pp.221-265, 1974.

, Logica Universalis: Towards a General Theory of Logic, 2007.

, Universal Logic: An Anthology -From Paul Hertz to Dov Gabbay, 2012.

, The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol.I, 2015.

R. Brady, , 2006.

L. Dubois, Lambda Theory: introduction of a constant for "nothing" into set theory, a model of consistency and most noticeable conclusions, Logique et Analyse, vol.56, issue.222, pp.165-181, 2013.

R. L. Epstein, Critical Thinking, 1998.

R. L. Epstein, Five Ways of Saying "Therefore": Arguments, Proofs, Conditionals, Cause and Effect, Explanations, 2001.

S. Krajewski, Wnioskowania prawomocne i mocne: jednolite podej´sciepodej´scie do wnioskowa´nwnioskowa´n niezawodnych i uprawdopodobniaj acych, Identycznosc znaku czy znak identycznosci, pp.247-254, 2012.

S. Krajewski, All Quantifiers versus the Quantifier All, The LvovWarsaw School. Past and Present, 2018.

C. Areces, P. Blackburn, A. Huertas, and &. Manzano, Completeness in Hybrid Type Theory, Journal of Philosophical Logic, vol.43, issue.2-3, pp.209-238, 2014.

M. Manzano, M. A. Martins, and &. Huertas, Completeness in Equational Hybrid Propositional Type Theory

M. C. Moreno, Intensions, Types and Existence, 2017.

S. Marcelino and &. Caleiro, Disjoint fibring of non-deterministic matrices, Logic, Language, Information, and Computation: 24th International Workshop, vol.10388, pp.242-255, 2017.

C. Caleiro and &. S. Marcelino, Fibring partial non-deterministic matrices, pp.60-63, 2017.

, This work was done under the scope of R&D Unit 50008, financed by the applicable financial framework (FCT/MEC through national funds and when applicable

S. Marcelino and &. Caleiro, Decidability and complexity of fibred logics without shared connectives, Logic Journal of the IGPL, vol.24, issue.5, pp.673-707, 2016.

S. Marcelino and &. Caleiro, Disjoint fibring of non-deterministic matrices, Logic, Language, Information, and Computation: 24th International Workshop, vol.10388, pp.242-255, 2017.

C. Caleiro, S. Marcelino, and &. Rivieccio, Plug and play negations, Studia Logica, special volume on

, This work was done under the scope of R&D Unit 50008, financed by the applicable financial framework (FCT/MEC through national funds and when applicable

C. Caleiro, S. Marcelino, and &. J. Marcos, Merging Fragments of Classical Logic, International Symposium on Frontiers of Combining Systems, vol.10483, pp.298-315, 2017.

C. Caleiro and &. S. Marcelino, Fibring partial non-deterministic matrices, pp.60-63, 2017.

M. Nowak, A syntactic approach to closure operation, Bulletin of the Section of Logic, vol.46, issue.3-4, pp.219-232, 2017.

D. J. Shoesmith-&-t and . Smiley, Multiple-conclusion Logic, 1978.

J. Zygmunt, An Essay in Matrix Semantics for Consequence Relations, Wydawnictwo Uniwersytetu Wrocc lawskiego, Wrocc law, 1984.

F. Berto, A Modality Called 'Negation', vol.124, pp.761-793, 2015.

J. Béziau, Bivalence, excluded middle and non contradiction, The Logica Yearbook, pp.73-84, 2003.

J. Béziau, Classical negation can be expressed by one of its halves, Logic Journal of the IGPL *, vol.7, issue.2, pp.145-151, 1999.

J. Béziau, S5 is a paraconsistent logic and so is first-order classical logic, Logical Investigations, vol.9, pp.301-309, 2002.

J. Béziau, A new four-valued approach to modal logic, Logique et Analyse, vol.54, issue.213, pp.109-121, 2011.

J. Dugundji, Note on a property of matrices for Lewis and Langford's calculi of propositions, The Journal of Symbolic Logic, vol.5, issue.4, pp.150-151, 1940.

J. M. Font and &. Hajek, On Lukasiewicz's four-valued logic, Studia Logica, vol.70, pp.157-182, 2002.

J. Lukasiewicz, A system of modal logic, Journal of Computing Systems, vol.1, issue.3, pp.111-149, 1953.

R. , Four-valued tables and modal logic, Notre Dame Journal of Formal Logic, vol.11, pp.505-511, 1970.

F. Schang and &. Costa-leite, Une sémantique générale des croyances justifiées, vol.16, pp.1-24, 2016.

C. Mclarty, Elementary Categories, Elementary Toposes, 1992.

C. Mortensen, Inconsistent Mathematics, 1995.

L. Estrada-gonzález, From (Paraconsistent) Topos Logic to Universal (Topos) Logic, The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol.II, pp.263-296, 2015.

C. Rauszer, An algebraic and Kripke-style approach to a certain extension of intuitionistic logic, Dissertationes Mathematicae, vol.167, p.61, 1980.

V. L. Vasyukov, Structuring the Universe of Universal Logic, Logica Universalis, vol.1, issue.2, pp.277-294, 2007.

J. C. Agudelo-agudelo and &. W. Carnielli, Polynomial ring calculus for modal logics: a new semantics and proof method for modalities, The Review of Symbolic Logic, vol.4, issue.1, pp.150-170, 2011.

J. C. Agudelo-agudelo and &. W. Carnielli, Polynomial ring calculus for modalities, Journal of Logic and Computation, vol.27, issue.6, pp.1853-1870, 2017.

J. C. Agudelo-agudelo, C. A. Agudelo-gonzález, and &. O. García-quintero, On polynomial semantics for propositional logics, Journal of Applied Non-Classical Logics, vol.26, issue.2, pp.103-125, 2016.

O. Arieli and C. Straßer, Sequent-based logical argumentation, Argument and Computation, vol.6, issue.1, pp.73-99, 2015.

A. Avron, A constructive analysis of RM, Symbolic Logic, vol.52, pp.939-951, 1987.

P. Besnard and &. A. Hunter, A logic-based theory of deductive arguments, Artificial Intelligence, vol.128, issue.1-2, pp.203-235, 2001.

M. Caminada and L. Amgoud, On the evaluation of argumentation formalisms, Artificial Intelligence, vol.171, issue.5, pp.286-310, 2007.

G. Gentzen, UntersuchungenüberUntersuchungen¨Untersuchungenüber das logische Schließen I, II, Mathematische Zeitschrift, vol.39, pp.405-431, 1934.

J. Buridan, Treatise on Consequences, translation and Introduction by S. Read, 2014.

J. Buridan, Summulae de Dialectica, 2001.

F. Arntzenius, Gunk, topology and measure, Oxford Studies in Metaphysics, vol.4, pp.225-247, 2008.

. Ph, T. Balbiani, &. Tinchev, and . Vakarelov, Modal Logics for Regionbased Theories of Space, Fundamenta Informaticae, vol.81, issue.1-3, pp.29-82, 2007.

D. Vakarelov, Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics, Mathematical Problems from Applied Logic II: Logics for the XXIst Century, pp.267-348, 2007.

V. Lobovikov, An Axiomatization of Philosophical Epistemology, Tomsk State University Journal, Series: Philosophy, Sociology, Political Studies, vol.36, issue.4, pp.69-78, 2016.

K. Swi, Classical Conceptions of the Changeability of Situations and Things Represented in Formalized Languages, 2008.

K. Swi-etorzecka and &. J. Czermak, A Logic of Change with Modalities, Logique et Analyse, vol.52, issue.253, pp.511-527, 2011.

R. Fagin, J. Y. Halpern, Y. Y. Moses-&-m, and . Vardi, Reasoning About Knowledge, 1995.

I. Stoica, R. Morris, D. Liben-nowell, D. Karger, M. Kaashoek et al., Chord: A Scalable Peer-to-peer Lookup Service for Internet Applications, IEEE „ /ACM Transactions on Networking, vol.11, issue.1, pp.17-32, 2003.

S. Ja´skowskija´skowski, A propositional Calculus for inconsistent deductive systems, Studia Societatis Scientiarum Torunensis, Sectio A, vol.1, issue.5, pp.35-56, 1948.

S. Ja´skowskija´skowski, On the discussive conjunction in the propositional calculus for inconsistent deductive systems, O koniunkcji dyskusyjnej w rachunku zda´nzda´n dla systemów dedukcyjnych sprzecznych, vol.1, pp.57-59, 1949.

J. Kotas, The axiomatization of S. Ja´skowskiJa´skowski's discussive system, Studia Logica, vol.33, issue.2, pp.195-200, 1974.

K. Mruczek-nasieniewska, M. Nasieniewski, and &. Pietruszczak, A modal logic over Ja´skowskiJa´skowski's discussive logic D 2

M. Nasieniewski and &. Pietruszczak, A method of generating modal logics defining Ja´skowskiJa´skowski's discussive logic D 2, Studia Logica, vol.97, issue.1, pp.161-182, 2011.

R. Girle, , 2009.

J. Gardies, Essai sur la logique des modalités, 1979.

P. Balbiani, T. Tinchev, and &. Vakarelov, Modal Logics for Regionbased Theories of Space, Fundamenta Informaticae, vol.81, issue.1-3, pp.29-82, 2008.

I. Düntsch and &. Vakarelov, Region-Based Theory of Discrete Spaces: A Proximity Approach, Proceedings of Fourth International Conference Journées de l'Informatique Messine, vol.49, pp.5-14, 2003.

. Ph, D. Balbiani, &. Georgiev, and . Tinchev, Modal correspondence theory in the class of all Euclidean frames, Journal of Logic and Computation

. Ph, &. Balbiani, and . Tinchev, Decidability and complexity of definability within the class of all partitions, 5th Panhellenic Logic Symposium, pp.26-33, 2005.

A. Chagrov and &. Chagrova, The Truth About Algorithmic Problems in Correspondence Theory, Advances in Modal Logic, vol.6, pp.121-138, 2006.

D. Georgiev, Definability in the class of all KD45-frames computability and complexity, Journal of Applied Non-Classical Logics

A. Aliseda, Abductive Reasoning: Logical Investigations into Discovery and Explanation, 2006.

P. Bonzon, M. Cavalcanti, and &. Nossum, Formal Aspects of Context, 2000.

, The Reach of Abduction: Insight and Trial, A Practical Logic of Cognitive Systems, vol.2, 2005.

G. Garbini and &. O. Durand, Introduzione alle lingue semitiche, Paideia Editrice, 1994.

J. Hintikka, Inquiry as Inquiry: A Logic of Scientific Discovery, 1999.

E. Lipinski, Semitic Languages Outline of a Comparative Grammar, Orientalia Lovaniensia Analecta book series, vol.80, 2000.

S. Moscati, A. Spitaler, and E. Ullendorff-&-w.-von-soden, An Introduction to the Comparative Grammar of the Semitic Languages: Phonology and Morphology, Porta Linguarum Orientalium book series, vol.6, 1969.

C. Morgan and &. E. Mares, Conditional Probability, and Non-Triviality, vol.24, pp.455-467, 1995.

F. Lepage, Is Lewis's Triviality Result Actually a Triviality Result?, Logique et Analyse, vol.58, issue.231, pp.373-377, 2015.

C. Morgan, Canonical Models and Probabilistic Semantics, Logic, Probability and Science, pp.17-35, 2000.

R. Routley, R. K. Meyer, V. T. Plumwood-&-r, and . Brady, Relevant Logics and Their Rivals, vol.1, 1982.

R. Sylvan, Variations on da Costa C Systems and dual-intuitionistic logics I. Analyses of C ? and CC ?, Studia Logica, vol.49, issue.1, pp.47-65, 1990.

R. Sylvan and &. Plumwood, Non-normal relevant logics, Relevant Logics and Their Rivals, vol.2, pp.10-16, 2003.

Z. Pawlak, Theoretical Aspects of Reasoning about Data, 1991.

A. Avron and B. Konikowska, Rough Sets and 3-Valued Logics, Studia Logica, vol.90, pp.69-92, 2008.

Y. Nakayama, S. Akama, and &. Murai, Deduction System for Decision Logic based on Partial Semantics, The Eleventh International Conference on Advances in Semantic Processing, 2017.

J. Van-benthem, Partiality and Nonmonotonicity in Classical Logic, Logique et Analyse, vol.29, pp.225-247, 1986.

A. Urquhart, Basic Many-Valued Logic, Handbook of Philosophical Logic, vol.2, pp.249-295, 2001.

J. Béziau, The paraconsistent logic Z. A possible solution to Ja´sJa´s-kowski's problem, Logic and Logical Philosophy, vol.15, issue.2, pp.99-111, 2006.

K. Do?en, Negative Modal Operators in Intuitionistic Logic, Publications de L'Institut Mathématique, vol.35, pp.3-15, 1984.

J. Marcos, Nearly every normal modal logic is paranormal, Logique et Analyse, vol.48, pp.279-300, 2005.

K. Mruczek-nasieniewska and &. M. Nasieniewski, Syntactical and Semantical Characterization of a class of Paraconsistent Logics, Bulletin of the Section of Logic, vol.34, issue.4, pp.229-248, 2005.

K. Mruczek-nasieniewska and &. M. Nasieniewski, Béziau's logics obtained by means of quasi-regular logics, Bulletin of the Section of Logic, vol.38, pp.189-203, 2009.

R. E. Bellman-&-l and . Zadeh, Decision-Making in a Fuzzy Environment, Management Science, vol.17, issue.4, pp.141-164, 1970.

M. K. Chakraborty and &. S. Dutta, Graded consequence revisited, Fuzzy Sets and Systems, vol.161, issue.14, pp.1885-1905, 2010.

R. Parikh, A test for fuzzy logic, ACM * SIGACT „ News, vol.22, issue.3, pp.49-50, 1991.

R. Parikh, Vagueness and utility: The semantics of common nouns, Linguistics and Philosophy, vol.17, issue.6, pp.521-535, 1994.

F. Baader, D. Calvanese, D. L. Mcguinness, D. &. Nardi, and . Patelschneider, The Description Logic Handbook: Theory, Implementation and Applications, 2011.

E. H. Haeusler and &. Rademaker, On how kelsenian jurisprudence and intuitionistic logic help to avoid contrary-to-duty paradoxes in legal ontologies, Journal of Applied Non-Classical Logics, 2016.

J. Y. Halpern and &. Y. Moses, A guide to completeness and complexity for modal logics of knowledge and belief, Artificial Intelligence, vol.54, issue.3, pp.319-379, 1992.

E. J. Lemmon, Algebraic semantics for modal logics I, The Journal of Symbolic Logic, vol.31, issue.1, pp.46-65, 1966.

E. J. Lemmon, Algebraic semantics for modal logics II, The Journal of Symbolic Logic, vol.31, issue.2, pp.191-218, 1966.

L. M. De-moura, S. Kong, J. Avigad, F. Van-doorn, and &. J. Von-raumer, The Lean Theorem Prover (system description)", in 25th International Conference on Automated Deduction, pp.378-388, 2007.

A. Rademaker, A Proof Theory for Description Logics, 2010.

A. Rademaker, A Proof Theory for Description Logics, SpringerBriefs in Computer Science series, 2012.

A. R. Anderson-&-n and E. Belnap, The Logic of Relevance and Necessity, vol.I, 1975.

R. K. Meyer and &. Routley, Classical relevant logics I, Studia Logica, vol.32, issue.1, pp.51-66, 1973.

R. K. Meyer and &. Routley, Classical relevant logics II, Studia Logica, vol.33, issue.2, pp.183-194, 1974.

G. Robles and J. M. Méndez, Routley-Meyer ternary relational semantics for intuitionistic-type negations

R. Routley, R. K. Meyer, V. T. Plumwood-&-r, and . Brady, Relevant Logics and their Rivals, vol.1, 1982.

M. Essert, I. Kuzmanovi´ckuzmanovi´c, I. Vazler, and &. Zili´czili´c, Theory of M-system, Logic Journal of the IGPL *, vol.25, issue.5, pp.836-858, 2017.

Y. Shramko and &. Wansing, Some Useful 16-Valued Logics: How a Computer Network Should Think, Journal of Philosophical Logic, vol.34, issue.2, pp.121-153, 2005.

M. Sare, , 2000.

D. M. Gabbay and &. Woods, The Reach of Abduction: Insight and Trial, Practical Logic of Cognitive Systems, vol.2, 2005.

C. S. Peirce, Collected Papers of Charles Sanders Peirce, vol.8, pp.1931-1958

E. Beth, Mededelingen van de Knifelike Nederlandse Akademie van Wetenschappen, Semantic Entailment and Formal Derivability, vol.18, pp.309-342, 1955.

M. Caminada, On the Issue of Reinstatement in Argumentation, Logics in Artificial Intelligence: 10th European Conference, vol.4160, pp.111-123, 2006.

C. Cayrol, S. Doutre, and &. Mengin, Dialectical Proof Theories for the Credulous Preferred Semantics of Argumentation Frameworks, Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 6th European Conference, vol.2143, pp.668-679, 2001.

C. I. Chesñevar-&-g and . Simari, An Abstract Model for Computing Warrant in Skeptical Argumentation Frameworks, Proceedings of the 11th Workshop on Nonmonotonic Reasoning, pp.409-417, 2006.

C. I. Chesñevar-&-g and . Simari, A Lattice-based Approach to Computing Warranted Belief in Skeptical Argumentation Frameworks, Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp.280-285, 2007.

P. M. Dung, On the Acceptability of Arguments and its Fundamental Role in Non-Monotonic Reasoning, Logic Programming and n-Person Games, Artificial Intelligence, vol.77, issue.2, p.41, 1995.

H. Jakobovits and &. Vermeir, Robust Semantics for Argumentation Frameworks, Journal of Logic and Computation, vol.9, issue.2, pp.215-261, 1999.

R. Smullyan, First Order-Logic, 1998.

G. Vreeswijk-&-h.-prakken, Credulous and Sceptical Argument Games for Preferred Semantics, Logics in Artificial Intelligence: European Workshop, vol.1919, pp.239-253, 2000.

S. Kearns and &. D. Star, Reasons as evidence, Oxford Studies in Metaethics, vol.4, pp.215-242, 2009.

D. Godden and &. Zenker, A probabilistic analysis of argument cogency, Synthese, vol.195, issue.4, pp.1715-1740, 2018.

W. Spohn, The Laws of Belief, 2012.

F. Zenker, Philosophical Quaterly, vol.65, issue.259, pp.310-313, 2014.

F. Zenker, Denying the Antecedent Probabilized: a Dialectical View, Proceedings of the 8th International Conference of the International Society for the Study of Argumentation, pp.1-14, 2014.

J. Desclés, G. Guibert, and &. Sauzay, Logique Combinatoire et ?-Calcul: des logiques d'opérateurs,Cépadù esÉditionses´esÉditions, 2016.

J. R. Hindley and &. P. Seldin, Lambda-Calculus and Combinators: An Introduction, 2008.

J. Desclés, G. Guibert, and &. Sauzay, Calculs de significations par une logique d'opérateurs,Cépadù esÉditionses´esÉditions, 2016.

J. Van-bethem, The Lambek Calculus, Categorial Grammars and Natural Language Structures, pp.35-68, 1988.

F. De-saussure, , 1983.

R. Jakobson, Essais de Linguistique Générale 1, 1963.

. Cl and . Lévi-strauss, Les structuresélémentairesstructuresélémentaires de la parenté, Presses Universitaires de France, 1967.

M. Manzano and &. E. Alonso, Completeness: from Gödel to Henkin, History and Philosophy of Logic, vol.35, pp.50-75, 2013.
DOI : 10.1080/01445340.2013.816555

E. Post, Introduction to a general theory of elementary propositions, pp.264-283, 1921.

P. Bernays, Beiträge zur axiomatischen Behandlung des Logik-Kalküls, pp.231-271, 1918.

L. Wittgenstein, Tractatus Logico-Philosophicus, 1922.

, From Frege to Gödel: a Source Book in Mathematical Logic, pp.1879-1931, 1967.

, David Hilbert's lectures on the Foundations of Arithmetic and Logic, 1917.

J. Girard, Interprétation fonctionnelle etéliminationetélimination des coupures de l'arithmétique d'ordre supérieur, 1972.

J. C. Reynolds, Towards a theory of type structure, Programming Symposium, vol.19, pp.408-425, 1974.

H. Hi?, The Journal of Symbolic Logic, vol.16, pp.58-59, 1951.

T. Jarmu? and &. M. Tkaczyk, Normalne logiki pozycyjne (Normal positional logics), 2015.

J. Lo´slo´s, Logiki wielowarto´sciowewielowarto´sciowe a formalizacja funkcji intensjonalnych, Multivalued logics vs. intensional functions formalization), vol.17, pp.59-78, 1948.

J. Lo´slo´s, Podstawy analizy metodologicznej kanonów Milla" (Basics of methodological analysis of Mill's canons), Sectio F, vol.2, pp.269-301, 1948.

A. Prior, Formal Logic, 1955.

N. Rescher and &. Urquhart, Temporal Logic, 1971.

R. Suszko and R. Of, Many-Valued Logics and the Formalization of Intensional Functions, The Journal of Symbolic Logic, vol.14, issue.1, pp.64-65, 1949.

T. Jarmu?, Tableau Metatheorem for Modal Logics, Recent Trends in Philosophical Logic, vol.41, pp.103-126, 2014.

H. Andréka, J. X. Madarász, and &. Németi, On the logical structure of relativity theories, research report, Alfréd Rényi Institute of Mathematics, 2002.

K. Lefever, Using Logical Interpretation and Definitional Equivalence to Compare Classical Kinematics and Special Relativity Theory, 2017.

K. Lefever and &. Székely, Comparing Classical and Relativistic Kinematics in First-Order Logic, 2018.

A. N. Whitehead, &. B. Russell, and P. Mathematica, , vol.1, 1910.

M. Fitting, T. Types, and . Gödel's-god, , 2002.

M. Gardner, Logic Machines and Diagrams, 1982.

D. D. Roberts, The Existential Graphs of Charles S. Pierce, Mouton, The Hague, 1973.

J. Desclés, Schèmes et topologie (de KantàKantà la sémantique cognitive), Colloque Histoire des mathématiques et sciences sociales, ´ Ecole des HautesÉtudesHautes´HautesÉtudes en Sciences Sociales, 2009.

J. C. Desclés-&-a and . Pascu, Logique de la Détermination des Objets (LDO): structuration topologique et quasi-topologique des extensions, 2016.

M. Abadi, L. Cardelli, P. Curien, and &. Levy, Explicit substitutions, Journal of Functional Programming, vol.1, issue.4, pp.375-416, 1991.
URL : https://hal.archives-ouvertes.fr/inria-00075382

J. Raclavsk´yraclavsk´y, P. Kuchy?ka, and &. Pezlar, Transparent Intensional Logic as Characteristica Universalis and Calculus Ratiocinator, 2015.

P. Tich´ytich´y, Foundations of Partial Type Theory, Reports on Mathematical Logic, vol.14, pp.59-72, 1982.

P. Tich´ytich´y, Indiscernibility of Identicals, Studia Logica, vol.45, issue.3, pp.251-273, 1986.

P. Tich´ytich´y, The Foundations of Frege's Logic, De Gruyter, 1988.

K. Brünnler, Deep sequent systems for modal logic, Archive for Mathematical Logic, vol.48, issue.6, pp.551-577, 2009.

K. Chaudhuri, S. Marin, and &. Straßburger, Focused and synthetic nested sequents, Proceedings of the 19th International Conference on Foundations of Software Science and Computation Structures, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01417618

K. Chaudhuri, S. Marin, and &. Straßburger, Modular focused proof systems for intuitionistic modal logics, 1st International Conference on Formal Structures for Computation and Deduction, vol.52, pp.1-16, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01417603

S. Marin, Modal proof theory through a focused telescope, 2018.
URL : https://hal.archives-ouvertes.fr/tel-01951291

S. Marin and &. Straßburger, Label-free Modular Systems for Classical and Intuitionistic Modal Logics, Advances in Modal Logic, vol.10, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01092148

L. Straßburger, Cut elimination in nested sequents for intuitionistic modal logics, 16th International Conference on Foundations of Software Science and Computation Structures, vol.7794, pp.209-224, 2013.

M. Bunder, Set Theory Based on Combinatory Logic, 1969.

O. Caramello and &. Lafforgue, Sur la dualité des topos et de leurs présentations et applications: une introduction, Institut des HautesÉtudes Hautes´HautesÉtudes Scientifiques, IHES/M/16/26, 2016.

G. Guibert, Two additional binary predicates "PP" and "O", whose intended meanings are respectively "being a proper part of" and "overlapping", can be defined as follows. PPxy = Pxy ? ¬Pyx and Oxy = ?z (Pzx ? Pzy). complementation" (GC): ?x (¬?y Pyx ? ?z ?w (Pwz ? ¬Owx)). is another axiom called, A Logical Trinity of Rational Ideas Across a Logic of Operators, 2017.

, Owx ? Owz))))

R. C. Casati-&-a and . Varzi, Parts and Places, 1999.

H. Tsai, Notes on Models of First-Order Mereological Theories, Logic and Logical Philosophy, vol.24, issue.4, pp.469-482, 2015.

/. Llp,

J. L. Chandler, Algebraic biology, Axiomathes, vol.19, issue.3, pp.297-320, 2009.

J. L. Chandler, An introduction to the perplex number system, Discrete Applied Mathematics, vol.157, pp.2296-2309, 2009.

J. L. Chandler, Organic Mathematics: On the Extension of Logics from Physical Atoms to Cellular Information Processes, Information Processing in Cells and Tissues, 10th International Conference, pp.29-35, 2015.

J. L. Chandler, An Introduction to the Foundations of Chemical Information Theory. Tarski-Le´sniewskiLe´sniewski Logical Structures and the Organization of Natural Sorts and Kinds, Information, vol.8, issue.1, 2017.

C. Sanders and P. , The Collected Papers of Charles Sanders Peirce, Elements of Logic, vol.2, 1931.

M. V. Kritz, Boundaries, interactions and environmental systems, Mecánica Computacional, vol.29, issue.26, pp.2673-2687, 2010.

G. J. Klir, Facets of Systems Science, 2001.

M. V. Kritz and &. Beziau, Théorie et modèle II, Cadernos UFS de Filosofia, vol.10, pp.7-16, 2011.

M. V. Kritz, From systems to organisations, Systems, vol.5, issue.1, 2017.

A. J. Ayer, Language, Truth and Logic, 2001.

G. Frege, The Foundations of Arithmetics: A Logico-Mathematical Enquiry into the Concept of Number, 1980.

I. Kant, Critique of Pure Reason, 1999.

S. A. Kripke, Naming and necessity, 1999.

H. Putnam, The Analytic and the Synthetic, Mind, Language and Reality: Philosophical Papers, pp.33-69, 1975.

W. V. Quine, Two Dogmas of Empiricism, The Philosophical Review, vol.60, pp.20-43, 1951.

G. Schurz, The Is-Ought Problem: An Investigation in Philosophical Logic, Studia Logica, vol.65, issue.3, pp.432-434, 2000.

S. Soames and ;. Lukowski, An approach to the liar paradox, New Aspects in NonClassical Logics and Their Kripke Semantics, pp.68-80, 1997.

P. Lukowski, Paradoxes, 2011.

A. N. Prior, On a family of paradoxes, Notre Dame Journal of Formal Logic, vol.2, issue.1, pp.16-32, 1961.

S. Rahman, T. Tulenheimo, and &. E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01249659

S. Read, Thinking about Logic: An Introduction to the Philosophy of Logic, 1995.

J. Macfarlane, In What Sense (If Any) Is Logic Normative for Thought?, Central Division * Meeting, Symposium on the Normativity of Logic, 2004.

D. Bonnay and &. Cozic, Which Logic for the Radical Antirealist?, The Realism-Antirealism Debate in the Age of Alternative Logics, pp.47-67, 2012.
URL : https://hal.archives-ouvertes.fr/halshs-00791838

J. Dubucs and &. M. Marion, Strict Antirealism and Substructural Logics, Philosophical Dimensions of Logic and Science, pp.235-249, 2004.
URL : https://hal.archives-ouvertes.fr/halshs-00790913

M. Dummett, The Philosophical Basis of Intuitionistic Logic, Truth and Other Enigmas, pp.215-247, 1973.

C. Wright, Strict Finitism, Realism, Meaning and Truth, pp.107-175, 1982.

W. Künne, Are Questions Propositions?, Revue Internationale de Philosophie, vol.224, pp.45-56, 2003.

J. Groenendijk and &. Stokhof, Questions, The Handbook of Logic and Language, pp.1055-1124, 1997.

L. Aqvist, Revised foundations for imperative-epistemic and interrogative logic, Theoria, vol.37, issue.1, pp.33-73, 1971.

B. Wolniewicz, Logic and Metaphysics, Znak-J¸ezykJ¸ezyk-Rzeczywisto´s´cRzeczywisto´s´Rzeczywisto´s´c, Warsaw, 1999.

V. L. Vasyukov, Structuring the Universe of Universal Logic, Logica Universalis, vol.1, issue.2, pp.277-294, 2007.

L. Wittgenstein and C. , Granger, Gallimard, 1914.

N. A. Vasiliev, Logic and Metalogic, Axiomathes, vol.4, issue.3, pp.329-351, 1993.

F. Didehvar, A Semantic Situation without Syntax (Non axiomatizability of Theories), Handbook of the 5th World Congress and School on Universal Logic, pp.307-311, 2015.

F. Didehvar, Is Classical Mathematics Appropriate for Theory of Computation?, 2017.

F. Didehvar, When the proof doesn't show the truth, World Philosophy Day, pp.153-161, 2010.

R. Lipton, The P = NP Question and Gödel's Lost Letter, 2010.

M. Nikitchenko and &. Chentsov, Basics of Intensionalized Data: Presets, Sets, and Nominats, Computer Science Journal of Moldova, vol.20, issue.3, pp.334-365, 2012.

V. Gavryluk and &. Nikitchenko, Philosophical Aspects of Programming Theory Development, Handbook of the 5th World Congress and School on Universal Logic, pp.210-211, 2015.

M. Nikitchenko and &. S. Shkilniak, Algebras and logics of partial quasiary predicates, Algebra and Discrete Mathematics, vol.23, issue.2, pp.263-278, 2017.

A. Kryvolap, M. Nikitchenko, and &. Schreiner, Extending Floyd-Hoare Logic for Partial Pre-and Postconditions, ICTERI 2013 * , Communications in Computer and Information Science book series, vol.412, pp.355-378, 2013.

J. Peregrin and &. Svoboda, Reflective Equilibrium and the Principles of Logical Analysis, Routledge, 2017.

A. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, vol.2, issue.42, pp.230-65, 1936.

J. A. Goguen, J. W. Thatcher, E. G. Wagner, and &. B. Wright, A Junction Between Computer Science and Category Theory (parts I and II

J. Thomas, . Watson-research, and . Center, , 1973.

C. F. Nourani, Slalom tree computing -a tree computing theory for artificial intelligence, AI Communications, vol.9, issue.4, pp.207-213, 1996.

C. F. Nourani, A Functorial Model Theory: Newer Applications to Algebraic Topology, Descriptive Sets, and Topos Computability, 2014.

C. F. Nourani, A Preliminary brief on direct product language models, memo, 2014.

C. F. Nourani and &. Eklund, Fragment functors and term constructible sets, AMS * -MAA „ Joint Meeting, 2014.

C. F. Nourani and &. Fähndrich, Factors on Signatured Trees and Semantic Language Processing, 2014.

M. Nikitchenko and &. Tymofieiev, Satisfiability in Composition-Nominative Logics, Central European Journal of Computer Science, vol.2, issue.3, pp.194-213, 2012.

M. Nikitchenko and &. S. Shkilniak, Algebras and logics of partial quasiary predicates, Algebra and Discrete Mathematics, vol.23, issue.2, pp.263-278, 2017.

C. Cohen, T. Coquand, S. Huber, and &. Mörtberg, Cubical Type Theory: a constructive interpretation of the univalence axiom, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01378906

P. Suppes, Representation and Invariance of Scientific Structures, 2002.

M. Makkai, Generalized sketches as a framework for completeness theorems. Part I, Journal of Pure and Applied Algebra, vol.115, issue.1, pp.7-9, 1997.

M. Makkai, Generalized sketches as a framework for completeness theorems. Part II, Journal of Pure and Applied Algebra, vol.115, issue.2, pp.179-212, 1997.

M. Makkai, Generalized sketches as a framework for completeness theorems. Part III, Journal of Pure and Applied Algebra, vol.115, issue.3, pp.241-274, 1997.

Z. Diskin and &. Wolter, A Diagrammatic Logic for Object-Oriented Visual Modeling, Electronic Notes in Theoretical Computer Science, vol.203, issue.6, pp.19-41, 2008.

A. Rutle, A. Rossini, Y. Lamo, and &. Wolter, A formal approach to the specification and transformation of constraints in MDE, The Journal of Logic and Algebraic Programming, vol.81, issue.4, pp.422-457, 2012.

Z. Diskin, Towards algebraic graph-based model theory for computer science, Bulletin of Symbolic Logic, vol.3, pp.144-145, 1997.

U. Wolter, Z. Diskin, and &. König, Graph Operations and Free Graph Algebras, Graph Transformation, Specifications, and Nets, vol.10800, pp.313-331, 2017.

, History The keynote speaker at this session is Anne-Françoise Schmid, p.159

, Logic Functions in the Philosophy of Al-Farabi

, the second outstanding representative of the Muslim peripatetic after al Kindi (801-873 AD), was born in Turkestan about 870 AD. Al-Farabi's studies commenced in Farab, then he travelled to Baghdad, other sciences, he came to be known as the "Second Teacher, Aristotle being the first. One of Al-Farabi's most important contributions was clarifying the functions of logic as follows

, He defined logic and compared it with grammar, and discussed the classification and fundamental principles of science in a unique and useful manner

, He made the study of logic easier by dividing it into two categories: Takhayyul (idea) and Thubut (proof)

, and in others, and faults that others find in us

, He said that if we do not comprehend logic, we must either have faith in all people, or mistrust all people, or differentiate between them

, In this paper, I will analyse the functions of logic in Al-Farabi's works, Enumeration of the Sciences, Book on the Syllogism

A. , Ihsa' al-'ulum (Enumeration of the Sciences), investigated by, 1968.

A. , Al-Farabi's Commentary and Short Treatise on Aristotle's De Interpretation, 1981.

J. Allwood, L. Andersson, and &. Dahl, Logic in Linguistics, 1979.

O. Bakar, Classification of Knowledge in Islam: A Study in Islamic Philosophies of Science, 1998.

J. Van-ess, The Logical Structure of Islamic Theology, Logic in Classical Islamic Culture, 1970.

A. , The Works of Aristotle, 1951.

G. Boole, An Investigation of the Law of Thought (1854)

J. Lukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, 1957.

J. Corcoran, Aristotle's demonstrative logic, History and Philosophy of Logic, vol.30, pp.1-20, 2009.

, Does the Metalogic that Underlies the Aristotelian Logic Resemble what Timothy Williamson Calls a "Folk Logic

, However relevant for Etchemendy's understanding of Tarski, Kaplan's view on the uninformativeness of logic, and Dummett's contempt for abductive methods in logic, Mancosu's and Williamson's criticisms, at least if I am right, leave a great part of traditional logic intangible

. Implicitly, syllogistic does not encourage views akin to what Williamson calls "folk logic" -at least if syllogistic is properly understood. deviations. Also in the realm of classical logic, Aristotle saw valid inferences as fulfilling some prerequisites that are informative, substantial or

A. Aristotle, . Priora, and . Posteriora, , 1964.

J. Etchemendy, Tarski on Truth and Logical Consequence, vol.53, pp.51-79, 1988.

J. Etchemendy, The Concept of Logical Consequence, 1990.

J. Etchemendy, Reflections on Consequence, New Essays on Tarski and Philosophy, pp.263-299, 2008.

P. Mancosu, The Architecture of Modern Mathematics. Essays in History and Philosophy, pp.209-237, 2006.

P. Mancosu, Fixed-versus Variable-domain Interpretations of Tarski's Account of Logical Consequence, Philosophy Compass, vol.5, issue.9, pp.745-759, 2010.

A. Tarski, Actes du Congrès International de Philosophie Scientifique, VII Logique, Actualités Scientifiques et Industrielles, vol.394, pp.1-11, 1936.

T. Williamson, Logics as Scientific Theories, at the Munich Center of Mathematical Philosophy, 2011.

T. Williamson, Logics as Scientific Theories, in the Parliament Hall of St. Andrews, Arché Workshop: The Epistemology of Logic, 2011.

T. Williamson, Logics as Scientific Theories, 2012.

P. M. Healey, Understandings of Logic Sublated by the Dialectic, Philosophy Study, vol.4, pp.41-54, 2014.

P. M. Healey, Squaring the Dialectic of Inference and Chance, Philosophy Study, vol.5, pp.257-271, 2015.

K. Boer, Hegel's Account of Contradiction in the Science of Logic Reconsidered, Journal of the History of Philosophy, vol.48, issue.3, pp.345-373, 2010.

D. K. Lewis, A Subjectivist's Guide to Objective Chance, Philosophy of Probability: Contemporary Readings, pp.83-132, 1980.

D. K. Lewis, Humean Supervenience Debugged, vol.103, pp.473-490, 1994.

I. Kant, Lectures on Metaphysics, 1997.

A. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, 1937.

S. Cook, The P versus NP Problem, 2000.

Q. Sun, Gongsun Long Zi, English version, 2014.

F. Beiser, , 2005.

J. M. Dunn, A truth value semantics for modal logic, Studies in Logic and the Foundations of Mathematics, vol.68, pp.87-100, 1973.

N. P. Eisnor, Hegelian and Syllogistic Logic Compared, Boston University Libraries, 1947.

G. W. Hegel, The Science of Logic, pp.1812-1816, 2010.

G. W. Hegel, Hegel's Logic: Part One of the Encyclopedia of the Philosophical Sciences, 1830.

P. Redding, The Role of Logic 'Commonly So Called' in Hegel's Science of Logic, British Journal for the History of Philosophy, vol.22, issue.2, pp.281-301, 2014.

A. and P. Analytics, The Complete Works of Aristotle, vol.II, 1984.

M. Storrs, of Handbook of The History of Logic, Logic: A History of its Central Concepts, vol.11, 2012.

R. B. Angell, Three Logics of Subjunctive Conditionals, presented at Colloquium on Logic and Foundations of Mathematics, vol.32, pp.556-557, 1966.

A. C. Graham, Later Mohist Logic, Ethics, and Science, 1978.

D. Mo, The Mozi: A Complete Translation, 2010.

M. Acclavio, A Constructive Proof of Coherence for Symmetric Monoidal Categories Using Rewriting, 2016.

A. Burroni, Higher-dimensional word problems with applications to equational logic, Theoretical Computer Science, vol.115, issue.1, pp.43-62, 1993.

Y. Guiraud, . Ph, and . Malbos, Coherence in monoidal track categories, Mathematical Structures in Computer Science, vol.22, issue.6, pp.931-969, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00470795

P. Arndt, R. Jansana, H. L. Mariano-&-d, and . Pinto, Finitary Filter pairs

W. J. Blok, &. Pigozzi, and A. Logics, , 1989.

A. Avron, Non-deterministic matrices and modular semantics of rules, Logica Universalis, pp.155-173, 2005.

W. A. Carnielli, M. E. Coniglio, and &. J. Marcos, Logics of Formal Inconsistency, Handbook of Philosophical Logic, vol.14, pp.1-93, 2007.

W. A. Carnielli-&-m and . Coniglio, Paraconsistent Logic: Consistency, Contradiction and Negation, vol.40, 2016.

M. E. Coniglio, A. Figallo-orellano, and &. A. Golzio, Non-deterministic algebraization of logics by swap structures, 2017.

R. Cignoli, The class of Kleene algebras satisfying an interpolation property and Nelson algebras, Algebra Universalis, vol.23, issue.3, pp.262-292, 1986.

M. M. Fidel, An algebraic study of a propositional system of Nelson, Proceedings of the First Brazilian Conference on Mathematical Logic, vol.39, pp.99-117, 1977.

D. Vakarelov, Notes on N-lattices and constructive logic with strong negation, Studia Logica, vol.36, issue.1-2, pp.109-125, 1977.

M. Aiguier-&-r and . Diaconescu, Stratified institutions and elementary homomorphisms, Information Processing Letters, vol.103, pp.5-13, 2007.

J. Barwise, Axioms for abstract model theory, Annnals of Mathematical Logic, vol.7, pp.221-265, 1974.

I. Bloch, Modal Logics on Mathematical Morphology for Qualitative Spatial Reasoning, Journal of Applied Non-Classical Logics, vol.12, pp.399-423, 2002.

I. Bloch, H. Heijmans, and &. Ronse, Mathematical Morphology, Handbook of Spatial Logics, pp.857-947, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00556180

I. Bloch and &. J. Lang, Towards mathematical morpho-logics, Technologies for Constructing Intelligent Systems, pp.367-380, 2002.

R. Diaconescu, Institution-independent Model Theory, 2008.

R. Diaconescu, Institutional semantics for many-valued logics, Fuzzy Sets and Systems, vol.218, pp.32-52, 2013.

J. A. Goguen and R. Burstall, Institutions: Abstract model theory for specification and programming, Journal of the ACM *, vol.39, issue.1, pp.95-146, 1992.

M. Giry, A categorical approach to probability theory, Categorical aspects of topology and analysis, vol.915, pp.68-85, 1981.

A. Jøsang, Artificial reasoning with subjective logic, Proceedings of the Second Australian Workshop on Commonsense Reasoning, 1997.

A. Jøsang, Generalising Bayes' Theorem in Subjective Logic, IEEE * International Conference on Multisensor Fusion and Integration for Intelligent Systems, 2016.

C. Aristotle, . Editions, and . Seuil, , 2002.

E. Benveniste, Catégories de pensée et catégories de langue, Pro-bì emes de Linguistique Générale, vol.1, pp.63-74, 1966.

O. Caramello and &. Lafforgue, Sur la dualité des topos et de leurs pré-sentations et applications: une introduction, Institut des HautesÉtudesHautes´HautesÉtudes Scientifiques, IHES/M/16/26, 2016.

J. Desclés, G. Guibert, and &. Sauzay, Calculs de signification par une logique d'opérateurs,Cépadù es, 2016.

N. Galatos, P. Jipsen, T. Kowalski, and &. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Studies in Logic and the Foundations of Mathematics book series, vol.151, 2007.

H. Hahn, Uber die nichtarchimedischen Größensysteme, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, vol.116, pp.601-655, 1907.

G. Metcalfe and &. Montagna, Substructural Fuzzy Logics, The Journal of Symbolic Logic, vol.72, issue.3, pp.834-864, 2007.

N. Lubomirsky, &. Castiglioni, and C. ,

S. Aguzzoli and &. S. Bova, The free n-generated BL-algebra, Annals of Pure and Applied Logic, vol.161, issue.9, pp.1144-1170, 2010.

S. Bova, BL-functions and Free BL-algebra, 2008.

M. Busaniche and &. Mundici, Geometry of Robinson consistency in Lukasiewicz logic, Annals of Pure and Applied Logic, vol.147, issue.1-2, pp.1-22, 2007.

P. Hájek, Metamathematics of Fuzzy Logic, 1998.

M. Amerbauer, Cut-free tableau calculi for some propositional normal modal logics, Studia Logica, vol.57, issue.2-3, pp.359-372, 1996.

P. Blackburn, M. De-rijke, and &. Y. Venema, Modal Logic, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00100503

M. Bo?i´bo?i´c-&-k.-do?en, Models for normal intuitionistic modal logics, Studia Logica, vol.43, issue.3, pp.217-245, 1984.

L. Esakia, The modalized Heyting calculus: a conservative modal extension of the intuitionistic logic, Journal of Applied Non-Classical Logics, vol.16, pp.349-366, 2006.

A. Muravitsky, Interconnection of the Lattices of Extensions of Four Logics, Logica Universalis, vol.11, issue.2, pp.253-281, 2017.

P. T. Johnstone, Sketches of an Elephant: A Topos Theory Compendium", two volumes, 2002.

E. Ochs and &. Arndt, Planar Heyting Algebras for Children, Geometric Morphisms, vol.3, 2017.

J. C. Baez, Quantum Quandaries: a Category-Theoretic Perspective, 2004.

B. Coecke, Introducing categories to the practicing physicist, 2008.

C. Heunen, An embedding theorem for Hilbert categories, Theory and Applications of Categories, vol.22, issue.13, pp.321-344, 2009.

M. Van-atten and O. Brouwer, Wadsworth Philosophers Series, 2004.

L. E. Brouwer, ¨ Uber Definitionsbereiche von Funktionen, Mathematische Annalen, vol.97, pp.60-75, 1927.

C. B. Boyer, The History of Calculus and Its Conceptual Development, 1959.

S. Dehaene, The Number Sense: How the Mind creates Mathematics, 1997.

E. R. Grosholz, Representation and Productive Ambiguity in Mathematics and Science, 2007.

T. Nickles, Discovery, A Companion to the Philosophy of Science, pp.85-96, 2000.

A. N. Whitehead, Process and Reality: An Essay in Cosmology, 1929.

M. Heather and &. Rossiter, Logical Monism: The Global Identity of Applicable Logic, Philosophia Mathematica, vol.14, issue.2, pp.39-52, 2006.

G. Cantor, Ueber eine elementare Frage der Mannigfaltigkeitslehre, On an Elementary Question of Set Theory), vol.1, pp.99-102

S. Lavine, Understanding the Infinite, 1994.

E. Sayan, What is Wrong with Cantor's Diagonal Argument?

E. Sayan, Contra Cantor: How to Count the "Uncountably Infinite

, Visual Images and Non-Deductive Rules in Mathematical Discovery Irina Starikova Postdoctoral Researcher

C. Cellucci, Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method, 2013.

M. Giaquinto, The Epistemology of Visual Thinking in Mathematics, 2016.

I. Lakatos, Proofs and Refutations, 1976.

, especially in the context of the enhanced indispensability argument. In the talk, I will focus on the last problem

. ˆ-didier-dubois, Model Theory and Mathematical Logic ˆ Francesca Poggiolesi (CNRS „ , IHPST ) -Proof Theory Louis Couturat, pp.1868-1914

, the 6th World Congress on Universal Logic, 2018.

S. French and &. Krause, Identity in Physics: A Historical, Philosophical and Formal Analysis, 2006.

D. Bochvar, On a three-valued calculus and its application in the analysis of the paradoxes of the extended functional calculus, Mathematicheskii Sbornik, vol.46, pp.287-308, 1938.

S. Bonzio, Duality for P lonka sums

S. Bonzio, J. Gil-férez, F. Paoli, and &. Peruzzi, On Paraconsistent Weak Kleene Logic: axiomatization and algebraic analysis, Studia Logica, vol.105, issue.2, pp.253-297, 2017.

S. Bonzio, A. Loi, and &. Peruzzi, A duality for involutive bisemilattices, Studia Logica, 2018.

J. Font, Abstract Algebraic Logic: An Introductory Textbook, 2016.

S. Halldén, The Logic of Nonsense, Lundequista Bokhandeln, 1949.

J. Lonka, On a method of construction of abstract algebras, Fundamenta Mathematicae, vol.61, issue.2, pp.183-189, 1967.

A. Romanowska and &. J. Smith, Modes, 2002.

W. Brown, Z. Gyenis, and &. Rédei, The modal logic of Bayesian belief revision, 2017.

Z. Gyenis, On the modal logic of Jeffrey conditionalization, 2018.

Z. Gyenis, Standard Bayes logic is not finitely axiomatizable, 2018.

Z. Gyenis and &. Rédei, General properties of Bayesian learning as a statistical inference determined by conditional expectations, The Review of Symbolic Logic, vol.10, issue.4, pp.719-755, 2017.

D. Lewis, On the Plurality of Worlds, 1986.

G. Priest, Towards Non-Being: The Logic and Metaphysics of Intentionality, 2016.

W. V. Quine, On What There Is, The Review of Metaphysics, vol.2, issue.5, pp.21-38, 1948.

, Winner of Bimal Krishna Matilal Logic Prize, p.573, 2018.

A. Avron, Natural 3-valued logics: Characterization and proof theory, The Journal of Symbolic Logic, vol.56, issue.1, pp.276-294, 1991.

N. D. Belnap, .. R. Anderson, N. D. Belnap, and .. M. Dunn, A useful four-valued logic: How a computer should think, Entailment: The Logic of Relevance and Necessity, vol.II, pp.30-56, 1977.

J. M. Dunn, Intuitive semantics for first-degree entailments and 'coupled trees', Philosophical Studies, vol.29, issue.3, pp.149-168, 1976.

F. J. Pelletier and &. Urquhart, Synonymous Logics, Journal of Philosophical Logic, vol.32, issue.3, pp.259-285, 2003.

F. J. Pelletier and &. Urquhart, Synonymous Logics: A Correction, Journal of Philosophical Logic, vol.37, issue.1, pp.95-100, 2008.

G. Priest, Contradiction: A Study of the Transconsistent, 2006.

N. Rescher, Many-Valued Logic, p.572, 1969.

D. Bonnay and &. Westerståhl, Consequence Mining: Constans Versus Consequence Relations, Journal of Philosophical Logic, vol.41, issue.4, pp.671-709, 2012.

M. Matos and &. J. Väänänen, Abstract model theory as a framework for universal logic, Logica Universalis: Towards a General Theory of Logic, pp.19-33, 2007.

, Natural Deduction for Regular Three-Valued Logics and their Four-Valued Analogues Yaroslav Petrukhin * Department of Logic, Faculty of Philosophy

, Winner of Vasiliev Logic Prize, p.573, 2018.

M. Fitting, Kleene's Three Valued Logics and Their Children, Fundamenta Informaticae, vol.20, pp.113-131, 1994.

S. C. Kleene, On a Notation for Ordinal Numbers, The Journal of Symbolic Logic, vol.3, issue.4, pp.150-155, 1938.

Y. I. Petrukhin, Natural Deduction for Three-Valued Regular Logics, Logic and Logical Philosophy, vol.26, issue.2, pp.197-206, 2017.

Y. I. Petrukhin, Natural Deduction for Fitting's Four-Valued Generalizations of Kleene's Logics, Logica Universalis, vol.11, issue.4, pp.525-532, 2017.

Y. I. Petrukhin, Natural Deduction for Four-Valued both Regular and Monotonic Logics, Logic and Logical Philosophy, vol.27, pp.53-66, 2018.

G. Priest, of Handbook of Philosophical Logic book series, Handbook of Philosophical Logic, vol.6, pp.287-393, 2002.

N. E. Tomova, About four-valued regular logics, Logical Investigations, vol.15, pp.223-228, 2009.

I. Varzinczak, *. Cril-„, C. Université-d'artois, F. Lens, and . Varzinczak@cril,

F. Baader, D. Calvanese, D. Mcguinness, D. Nardi, and &. Patel-schneider, The Description Logic Handbook: Theory, Implementation and Applications, 2007.

S. Kraus, D. Lehmann, and &. Magidor, Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, vol.44, issue.1-2, pp.167-207, 1990.

D. Lehmann and &. Magidor, What does a conditional knowledge base entail?, Artificial Intelligence, vol.55, issue.1, pp.1-60, 1992.

K. Schild, A correspondence theory for terminological logics: preliminary report, Proceedings of the 12th International Joint Conference on Artificial Intelligence, IJCAI'91, vol.1, pp.466-471, 1991.