Undefinability of Standard sequent calculi for Paraconsistent three-valued logics

Abstract

In this paper we study the deductive properties of a family of 3-valued paraconsistent logics. We define a notion of standard sequent calculus and prove that there is no sound and complete standard sequent calculus for these logics. Moreover, we provide non-standard sound, complete and cut free sequent calculus for Paraconsistent Weak Kleene Logic using three-sided sequents.

arXiv commentWe found out that the paper contains some obscure points that can be misleading for the reader; some results shall be revised, deleted and/or replaced. As this process could take long time we would like to withdraw the submission for the moment. Thank you for your comprehension