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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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20 Dec 2012
TL;DR: Paraconsistent logics have the property of being non-explosive, that is, it is not possible to infer any conclusion from contradictories premises as mentioned in this paper, which is a common ground for the discussion.
Abstract: This article begins with a general and abstract definition of logic and, particularly, of paraconsistent logics, to establish a common ground for the discussion. Briefly stating, these kinds of logics have the property of being non-explosive, that is, it is not possible to infer any conclusion from contradictories premises. Using these definitions, it is possible to analyze some of the philosophical aspects of paraconsistent logics, in particular, the relation between the notion of explosion and the law of non-contradiction, as well as the syntactic/semantic possibility and, above all, the metaphysical possibility of paraconsistent logics. I further analyze a stronger position towards paraconsistency, namely: the claim that there are true contradictions. This articles concludes with some possible critiques to paraconsistent logics – and their refutations as well –, and pose some open questions for further work.
Journal ArticleDOI
01 Oct 2021-Synthese
TL;DR: By showing that this logic is maximally paraconsistent, it is proved that CLP is the only logic satisfying all postulated desiderata and how the logic’s infinite-valued semantics permits defining different types of entailment relations.
Abstract: This paper is devoted to a consequence relation combining the negation of Classical Logic ($$\mathbf {CL}$$) and a paraconsistent negation based on Graham Priest’s Logic of Paradox ($$\mathbf {LP}$$). We give a number of natural desiderata for a logic $$\mathbf {L}$$ that combines both negations. They are motivated by a particular property-theoretic perspective on paraconsistency and are all about warranting that the combining logic has the same characteristics as the combined logics, without giving up on the radically paraconsistent nature of the paraconsistent negation. We devise the logic $$\mathbf {CLP}$$ by means of an axiomatization and three equivalent semantical characterizations (a non-deterministic semantics, an infinite-valued set-theoretic semantics and an infinite-valued semantics with integer numbers as values). By showing that this logic is maximally paraconsistent, we prove that $$\mathbf {CLP}$$ is the only logic satisfying all postulated desiderata. Finally we show how the logic’s infinite-valued semantics permits defining different types of entailment relations.
21 Nov 2014
TL;DR: The authors develop and motivate a paraconsistent approach to semantic paradox from within a modest inferentialist framework, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and via which, classical semantics can be determined.
Abstract: This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truth-predicate to motivate an intermediate speech-act. On this approach, a liar-like sentence should be "weakly asserted", involving a commitment to the sentence and its negation, without rejecting the sentence. From this, I develop a proof-theory, which both determines a typical paraconsistent model theory, and also gives us a nice way to understand classical recapture.
Book ChapterDOI
08 Sep 2010
TL;DR: The Curry monadic system N1 constitutes an algebraic version of the non-alethic predicate logic N1* which has as extensions the Curry monads C1* and P1*.
Abstract: This paper is a sequel to [5], [6]. We present the Curry monadic system N1* which has as extensions the Curry monadic algebras C1* and P1*. All those systems are extensions of the classical monadic algebras introduced by Halmos [13]. Also the Curry monadic system N1 constitutes an algebraic version of the non-alethic predicate logic N1*.
Journal ArticleDOI
TL;DR: The main tendenci es of development of modern logic are pointed out in this article, where the following questions are discussed: (i) What is logical consequence? (ii) What are logical constants (operations).
Abstract: In the paper the following questions are discussed: (i) What is logical consequence? (ii) What are logical constants (operations)? (iii) What is a log ical system? (iv) What is logical pluralism? (v) What is logic? In the conclusion, the main tendenci es of development of modern logic are pointed out.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202255
202131
202036
201935
201847