Sequent-Type Calculi for Systems of Nonmonotonic Paraconsistent Logics

Tobias Geibinger
Hans Tompits

Paraconsistent logics constitute an important class of formalisms dealing with non-trivial 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 sequent-type proof systems. The latter are prominent and widely-used forms of calculi well-suited for analysing proof search. In particular, we provide sequent-type calculi for Priest's three-valued minimally inconsistent logic of paradox, and for four-valued 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 so-called rejection calculus for axiomatising invalid formulas. In fact, we present a general method to obtain sequent systems for any many-valued logic based on minimal inconsistency, yielding the calculi for the logics of Priest and of Arieli and Avron as special instances.

In Francesco Ricca, Alessandra Russo, Sergio Greco, Nicola Leone, Alexander Artikis, Gerhard Friedrich, Paul Fodor, Angelika Kimmig, Francesca Lisi, Marco Maratea, Alessandra Mileo and Fabrizio Riguzzi: Proceedings 36th International Conference on Logic Programming (Technical Communications) (ICLP 2020), UNICAL, Rende (CS), Italy, 18-24th September 2020, Electronic Proceedings in Theoretical Computer Science 325, pp. 178–191.
Published: 19th September 2020.

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