Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Anderson's Relevant Deontic and Eubouliatic Systems

Abstract: We present axiomatizations of the deontic fragment of Anderson's relevant deontic logic (the logic of obligation and related concepts) and the eubouliatic fragment of Anderson's eubouliatic logic (the logic of prudence, safety, risk, and related concepts).

Rewriting the History of Connexive Logic

Abstract: Abstract The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties (like the condition that no proposition implies its own negation) only apply to “normal” (e.g., self-consistent) antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning (“humbly”) connexive implication don’t give rise, however, to anything like a non-classical logic.

On polynomial semantics for propositional logics

Abstract: Some properties and an algorithm for solving systems of multivariate polynomial equations over finite fields are presented. It is then shown how formulas of propositional logics (particularly of finite-valued logics and paraconsistent logics) can be translated into polynomials over finite fields in such a way that several logic problems are expressed in terms of algebraic problems. Consequently, algebraic properties and algorithms can be used to solve the algebraically-represented logic problems. The methods described herein combine and generalise those of various previous works.

Bibel's matrix connection method in paraconsistent logic: general concepts and implementation

Abstract: Bibel's matrix connection method is an alternative to resolution for the mechanized proof of logical statements. Bibel's method was originally defined for classical logic. In this work, an adaptation of the method for annotated propositional logic is given, followed by a simple case study. Some implementation details are also presented.

Formalizing Inconsistency-Tolerant Relevant Human Reasoning: A Decidable Paraconsistent Relevant Logic with Constructible Falsity

Abstract: Formalizing inconsistency-tolerant relevant human reasoning in a philosophically plausible logic is useful for modeling sophisticated agents similar to human. For this aim, the positive fragment of the logic RW of contraction-less relevant implication is extended with the addition of a Para consistent negation connective similar to the strong negation connective in Nelson's Para consistent four-valued logic N4. This extended para-consistent relevant logic is called RWP, and it has the property of constructible falsity which is known to be useful for representing inexact predicates. A Gentzen-type sequent calculus SRWP for RWP is introduced, and the decidability and cut-elimination theorems for SRWP are proved. An extended Routley-Meyer semantics is introduced for RWP, and the completeness theorem with respect to this semantics is proved.