Undefinability of Standard sequent calculi for Paraconsistent three-valued logics

2016/12/03 by Bonzio, S., Baldi, M. Pra
#03B53 #FOS: Mathematics #Logic (math.LO) #Primary 03F03. Secondary 03B50

paper · doi:10.48550/arxiv.1612.00963

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.

Related

• Paraconsistentization and many-valued logics
• Parametric mixed sequent calculus
• Sequent-Type Proof Systems for Three-Valued Default Logic
• A classical-logic view on a paraconsistent logic
• A Sequent Calculus and a Theorem Prover for Standard Conditional Logics