Open AccessProceedings Article
Maximally paraconsistent three-valued logics
Ofer Arieli,Arnon Avron,Anna Zamansky +2 more
- pp 310-318
TLDR
This paper introduces the strongest possible notion of maximal paraconsistency, and investigates it in the context of logics that are based on deterministic or non-deterministic three-valued matrices.Abstract:
Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives.read more
Citations
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Journal ArticleDOI
Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics
TL;DR: This paper shows that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in the authors' strong sense, and investigates the strongest possible notion of maximal paraconsistency, which is investigated in the context of logics that are based on deterministic or non-deterministicThree-valued matrices.
Journal ArticleDOI
A Note on Freedom from Detachment in the Logic of Paradox
TL;DR: It is shown that the logic LP cannot dene a binary connective obeying detachment in the sense that every valuation satisfying ' and ' also satises , except trivially, as a corollary of a more general result concerning variable-sharing.
Book ChapterDOI
Paraconsistent constructive logic with strong negation as a contraction-free relevant logic
Matthew Spinks,Robert Veroff +1 more
TL;DR: The notion of strong negation was introduced by Nelson's constructive logic with negation N4 (N4) as mentioned in this paper, an axiomatic expansion of the negation-free fragment of the intuitionistic propositional calculus (Rasiowa, 1974, Chapter X) by a unary logical connective.
Proceedings ArticleDOI
On Strong Maximality of Paraconsistent Finite-Valued Logics
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.
Proceedings Article
Propositional and Predicate Logics of Incomplete Information
TL;DR: This work imposes rationality conditions on the semantics of the connectives of the propositional logic, and proves that Kleene’s logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice.
References
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Book
Handbook of Philosophical Logic
Dov M. Gabbay,Franz Guenthner +1 more
TL;DR: This paper presents a meta-mathematicalPrinciples of Deductive Systems: Foundations to Meta-mathematicics Murdoch J. Gabbay, with a focus on the role of formal semantics in the development of deterministic systems.
Journal ArticleDOI
On the theory of inconsistent formal systems.
Book ChapterDOI
Logics of Formal Inconsistency
TL;DR: The Logicas da Inconsistencia Formal (LIFs) as mentioned in this paper form a classe of logicas paraconsistentes particularmente expressivas, in which a nocao meta-teonca de consistencia pode ser internalizada ao nivel da linguagem obje[c]to.