From paraconsistent three-valued logics to multiple-source epistemic logic

Davide Ciucci (1) , Didier Dubois (2, 3)

1 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 CNRS - Centre National de la Recherche Scientifique

Several interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent three-valued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appear in front of literals. This logic is unusual in the sense that necessity modalities distribute over disjunctions instead of conjunctions. An equivalent translation into a fragment of KD modal logic can be obtained by exchanging the role of possibility and necessity modalities, highlighting the perfect symmetry between three-valued logics of contradiction and three-valued logics of incomplete information.

Mots clés: Logic

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Davide Ciucci, Didier Dubois. From paraconsistent three-valued logics to multiple-source epistemic logic. 8th European Society For Fuzzy Logic And Technology Conference (EUSFLAT 2013), Sep 2013, Milan, Italy. pp. 780-787. ⟨hal-01212932⟩