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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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Journal Article
TL;DR: In this article, the authors show that the mental logic theory enables to understand why the Stoics considered the inference schemata to be basic kinds of arguments, which can explain why the last argument was included into the set of indemonstrables as well.
Abstract: Stoic logic assumes fi ve inference schemata attributed to Chrysippus of Soli. Those schemata are the well-known indemonstrables. A problem related to them can be that, according to standard propositional calculus, only one of them, modus ponens, is clearly indemonstrable. Nevertheless, I try to show in this paper that the mental logic theory enables to understand why the Stoics considered such schemata to be basic kinds of arguments. Following that theory, four of them can be linked to ‘Core Schemata’ of mental logic and the only one that is more controversial is modus tollens. However, as I also comment, some assumptions of Stoic philosophy, which can be interpreted from the mental logic theory, can explain why this last argument was included into the set of the indemonstrables as well.

12 citations

Journal ArticleDOI
TL;DR: The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc- logics.
Abstract: In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as "da Costa logic"). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined.

12 citations

Proceedings ArticleDOI
11 Jul 2010
TL;DR: This paper introduces a new, strong notion of maximal paraconsistency, which is based on possible extensions of the consequence relation of a logic, and investigates this notion in the framework of finite-valued paraconsistent logics.
Abstract: Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain as much as possible from classical logic. In this paper we introduce a new, strong notion of maximal paraconsistency, which is based on possible extensions of the consequence relation of a logic. We investigate this notion in the framework of finite-valued paraconsistent logics, and show that for every $n>2$ there exists an extensive family of $n$-valued logics, each of which is maximally paraconsistent in our sense, is partial to classical logic, and is not equivalent to any $k$-valued logic with $k

12 citations

Book ChapterDOI
25 Jul 2013
TL;DR: It is shown that, at least for this particular example, both the Bayesian and the quantum-like approaches have less normative power than the negative probabilities one.
Abstract: In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular example, both the Bayesian and the quantum-like approaches have less normative power than the negative probabilities one.

12 citations

Journal ArticleDOI
Arnon Avron1
TL;DR: This paper investigates quasi-canonical systems in which exactly one of the two classical rules for negation is included, turning the induced logic into either a paraconsistent logic or a paracomplete logic, but not both.
Abstract: A quasi-canonical Gentzen-type system is a Gentzen-type system in which each logical rule introduces either a formula of the form , or of the form , and all the active formulas of its premises belong to the set . In this paper we investigate quasi-canonical systems in which exactly one of the two classical rules for negation is included, turning the induced logic into either a paraconsistent logic or a paracomplete logic, but not both. We provide a constructive coherence criterion for such systems, and show that a quasi-canonical system of the type we investigate is coherent iff it is strongly paraconsistent or strongly paracomplete (in a sense defined in the paper), iff it has a trivalent, non-deterministic semantics of a special type (also defined in the paper) for which it is sound and complete. Finally, we determine when a system of this sort admits cut-elimination, and provide a simple procedure for transforming one which does not into one which does.

12 citations


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