Topic
Paraconsistent logic
About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.
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TL;DR: An extension of the Grothendieck topological semantics for BI is introduced for PBI, and the completeness theorem with respect to this semantics is proved.
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TL;DR: In this paper, the concept of a k-transform of a formula is discussed and some applications of its applications are considered in the context of paraconsistent logical systems and metamathematical properties of such systems are studied.
Abstract: We study some metamathematical properties of various classical and paraconsistent logical systems. In particular, we discuss the concept of a k-transform of a formula and consider some of its applications.
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TL;DR: It is proved that there is no sound and complete standard sequent calculus for these logics, so non-standard sound, complete and cut freesequent calculus is provided for Paraconsistent Weak Kleene Logic using three-sided sequents.
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.
1 citations