Depth relevance of some paraconsistent logics

Ross T. Brady

doi:10.1007/bf00935740

Useful Four-Valued Extension of the Temporal Logic KtT4

Bulletin of the Section of Logic ◽

10.18778/0138-0680.47.1.02 ◽

2018 ◽

Vol 47 (1) ◽

Cited By ~ 1

Author(s):

Vincent Degauquier

Keyword(s):

Modal Logic ◽

Temporal Logic ◽

Paraconsistent Logics ◽

Accessibility Relation

The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial and paraconsistent logics.

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Curry’s Paradox, Generalized Contraction Rule and Depth Relevance

Proceedings of the XXIII World Congress of Philosophy ◽

10.5840/wcp23201819491 ◽

2018 ◽

pp. 35-39

Author(s):

Francisco Salto ◽

Gemma Robles ◽

José M. Méndez

Keyword(s):

Generalized Contraction ◽

Curry’S Paradox ◽

Curry's Paradox ◽

Depth Relevance

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Consequence-Inconsistency Interderivability in Paraconsistent Logics and Paraconsistent Set Theory

Handbook of Logical Thought in India ◽

10.1007/978-81-322-1812-8_38-1 ◽

2020 ◽

pp. 1-35

Author(s):

Soma Dutta ◽

Sourav Tarafder

Keyword(s):

Set Theory ◽

Paraconsistent Logics

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Paraconsistency, self-extensionality, modality

Logic Journal of IGPL ◽

10.1093/jigpal/jzy064 ◽

2018 ◽

Vol 28 (5) ◽

pp. 851-880

Author(s):

Arnon Avron ◽

Anna Zamansky

Keyword(s):

Intuitionistic Logic ◽

Modal Logics ◽

The Other ◽

Paraconsistent Logics ◽

Classical Negation ◽

Inconsistent Theories ◽

Replacement Property ◽

General Method

Abstract Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.

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Paraconsistent Logics: Preamble

Paraconsistent Intelligent-Based Systems - Intelligent Systems Reference Library ◽

10.1007/978-3-319-19722-7_1 ◽

2015 ◽

pp. 1-22

Author(s):

Jair Minoro Abe

Keyword(s):

Paraconsistent Logics

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Logic and Philosophical Methodology

10.1093/oxfordhb/9780199668779.013.30 ◽

2016 ◽

Author(s):

John P. Burgess

Keyword(s):

Set Theory ◽

Model Theory ◽

Classical Logic ◽

Proof Theory ◽

Recursion Theory ◽

Theory Model ◽

Philosophical Methodology ◽

Paraconsistent Logics ◽

Philosophical Logic

This article explores the role of logic in philosophical methodology, as well as its application in philosophy. The discussion gives a roughly equal coverage to the seven branches of logic: elementary logic, set theory, model theory, recursion theory, proof theory, extraclassical logics, and anticlassical logics. Mathematical logic comprises set theory, model theory, recursion theory, and proof theory. Philosophical logic in the relevant sense is divided into the study of extensions of classical logic, such as modal or temporal or deontic or conditional logics, and the study of alternatives to classical logic, such as intuitionistic or quantum or partial or paraconsistent logics. The nonclassical consists of the extraclassical and the anticlassical, although the distinction is not clearcut.

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