?. Pef, According to Definition 3-16, we have 3 ? IIF( 1 ) ? RCS\{?} and, with Theorem 3-25, Therefore ? = ?)}. Thus we have AVAS( 3 ) = AVAS( 1 ), ? = ? ? (? ? ?) ? AVP( 2 ) ? AVP( 3 ) and ? = ? ?

*. Par\{?, Suppose Dom() = 0. Then we have = ? = [?*, ?, ] and thus

?. With and . Rce, Dom()-1) and Definition 3-18, we have that ? AF

?. With-?, ?. Par\stseq, and . Const, i )]), because, if not, we would have ? ? STSEQ() or ? = ?, which contradicts the hypothesis and Postulate 1-1 respectively. With a), it holds that f

C. Cdef, C. Bif, . Bef, . Dif, . Def et al., with which + is then in each case the desired RCS-element. In order to ease the treatment of, we will now first show that g) If + ? CdIF(*) ? NIF(*) ? PEF(*), then ? CdIF(Dom()-1) ? NIF(Dom()-1) ? PEF

+. Now, ?. Par, ?. ?. Var, and . Form, According to Definition 3-15 and with c), d) and f), there are then ?

N. Cdif and P. , Then we can make an exclusion assumption that allows us to determine Dom(AVS( + )) for all other cases just with c), g) and Theorem, pp.3-25

N. Cdif, Suppose ? CdIF(Dom()-1) According to Definition 3-2, there is then an i ? Dom(AVAS(Dom()-1)) such that there is no l ?

*. Par, ?. Var, and ?. Form, According to Definition 3-15, there are then ?, p.where FV

C. Cdef, . Bif, and . Bef, According to Theorem 3-28, we then have AVAP() = AVAP(Dom()-1) We can distinguish 13 subcases According to Definition 3-3, NIF, issue.11

. Then and . Dom, -1 such that B ? ? is available in Dom()-1 at j and B ? C() is available in Dom(
URL : https://hal.archives-ouvertes.fr/hal-01064314

P. , ?. Var, and ?. Form, where FV(?) ? {?}, such that

B. References and D. , Intermediate Logic (1997): Intermediate Logic

D. and O. Mengenlehre, Einführung in die Mengenlehre. Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo, 2004.

E. and H. Mengenlehre, Einführung in die Mengenlehre, 2003.

E. , H. Flum, J. Thomas, and W. M. Logik, Einführung in die mathematische Logik, 1996.

G. and K. M. Logik, Skriptum zur Vorlesung Mathematische Logik, Mathematisches Institut der Universität Heidelberg, 2006.

G. and E. M. Logik, Mathematische Logik. SS, Mathematische Grundlagen der Informatik. RWTH Aachen, 2009.

H. and P. Pragmatische-regeln, Pragmatische Regeln des logischen Argumentierens, Logik und Pragmatik. Frankfurt am Main: Suhrkamp, pp.199-215, 1982.

K. and R. Grundlagen-der-modernen-definitionstheorie, Grundlagen der modernen Definitionstheorie, 1979.

L. and G. C. Logicum, Collegium Logicum: Logische Grundlagen der Philosophie und der Wissenschaften . 2 volumes, Paderborn: Mentis, vol.1, 2009.

S. Shapiro and . Logic, et seqq.): Classical Logic The Stanford Encyclopedia of Philosophy, 2000.

S. and G. Vorfragen, Vorfragen zur Wahrheit, 1997.

S. and G. Denkwerkzeuge, et seqq.): Denkwerkzeuge. Eine Vorschule der Philosophie, 2002.

S. and G. A. Acts, Alethic Acts and Alethiological Reflection An Outline of a Constructive Philosophy of Truth Truth and speech acts. Studies in the philosophy of language, pp.41-58, 2007.

W. and H. L. Systeme, Logische Systeme der Informatik, WS, 2000.

1. Definition, *. , *. , and ?. , The set of expressions (EXP; metavariables: ?, ?

1. Definition, *. , and ?. , The set of terms (TERM; metavariables: ?, ?, p.13

1. ?. Definition, ?. , ?. , ?. , ?. '. et al., The set of formulas (FORM, p.13

1. .. Definition, Assignment of the set of variables that occur free in a term ? or in a formula ? (FV), p.22

1. Definition, The set of closed formulas (CFORM), p.23

1. Definition, ?. '. , ?. *. , and ?. , The set of sentences (SENT; metavariables: ?, p.23

1. Definition, The set of proper expressions (PEXP), p.24

1. Definition, The set of sentence sequences (SEQ), p.25

1. Definition, Assignment of the set of subterms of the members of a sequence (STSEQ), p.26

1. Definition, Assignment of the set of subterms of the elements of a set of formulas X (STSF), p.26

1. Definition, Substitution of closed terms for atomic terms in terms, formulas, sentences and sentence sequences, p.27

2. Definition, Assignment of the set of segments of (SG), p.50

2. Definition, Suitable sequences of natural numbers for subsets of sentence sequences, p.55

2. Definition, Segment sequences for sentence sequences, p.58

2. Definition, Assignment of the set of segment sequences for (, p.58

2. I. Definition and .. , AS?comprising segment sequence for a segment, p.61

2. Definition, Assignment of the set of AS?comprising segment sequences in (ASCS), p.61

2. Definition, Availability of a proposition in a sentence sequence at a position, p.104

2. Definition, Availability of a proposition in a sentence sequence, p.105

2. Definition, Assignment of the set of available sentences (AVS), p.105

2. Definition, Assignment of the set of available assumption?sentences (AVAS), p.105

2. Definition, Assignment of the set of available propositions (AVP), p.105

2. Definition, Assignment of the set of available assumptions (AVAP), p.105

3. Definition, The set of rule?compliant sentence sequences (RCS), p.135

3. Definition, The closure of a set of propositions under deductive consequence, p.142

5. Definition, Term denotation functions for models and parameter assignments, p.218

5. Definition, Satisfaction functions for models and parameter assignments, p.220

5. Definition, The closure of a set of propositions under model?theoretic consequence, p.234

6. Theorem, Correctness of the Speech Act Calculus relative to the model?theory, p.250

6. Theorem and .. L-h-l?entities, ?models and their L?restrictions behave in the same way with regard to, p.253

6. Theorem and .. L?satisfiable, A set of L?propositions is L H ?satisfiable if and only if it is, p.253

6. Theorem, L?sequences are RCS H ?elements if and only if they are RCS?elements, p.254

6. Theorem, An L?proposition is L H ?derivable from a set of L?propositions if and only if it is L?derivable from that set, p.254

6. Theorem and .. L?consistent, A set of L?propositions is L H ?consistent if and only if it is, p.255

3. Speech?act-rule, Rule of Conditional Introduction (CdI), p.123

3. Speech?act-rule, Rule of Conditional Elimination (CdE), p.124

3. Speech?act-rule, Rule of Conjunction Introduction (CI), p.124

3. Speech?act-rule, Rule of Biconditional Introduction (BI), p.124

3. Speech?act-rule, Rule of Negation Introduction (NI), p.125

3. Speech?act-rule, Rule of Particular?quantifier Introduction (PI), p.126

3. Speech?act-rule, Rule of Particular?quantifier Elimination (PE), p.126

3. Speech?act-rule, Rule of Identity Introduction (II), p.126