SequentType Calculi for Systems of Nonmonotonic Paraconsistent Logics
Abstract
Paraconsistent logics constitute an important class of formalisms dealing with nontrivial reasoning from inconsistent premisses. In this paper, we introduce uniform axiomatisations for a family of nonmonotonic paraconsistent logics based on minimal inconsistency in terms of sequenttype proof systems. The latter are prominent and widelyused forms of calculi wellsuited for analysing proof search. In particular, we provide sequenttype calculi for Priest's threevalued minimally inconsistent logic of paradox, and for fourvalued paraconsistent inference relations due to Arieli and Avron. Our calculi follow the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti and Olivetti, whose distinguishing feature is the use of a socalled rejection calculus for axiomatising invalid formulas. In fact, we present a general method to obtain sequent systems for any manyvalued logic based on minimal inconsistency, yielding the calculi for the logics of Priest and of Arieli and Avron as special instances.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 DOI:
 10.48550/arXiv.2009.10246
 arXiv:
 arXiv:2009.10246
 Bibcode:
 2020arXiv200910246G
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Artificial Intelligence;
 F.4.1;
 I.2.3;
 I.2.4
 EPrint:
 In Proceedings ICLP 2020, arXiv:2009.09158