Many-valued non-deterministic semantics for first-order logics of formal (In)consistency

Arnon Avron; Anna Zamansky

doi:10.1007/978-3-540-75939-3_1

Many-valued non-deterministic semantics for first-order logics of formal (In)consistency

Arnon Avron^*, Anna Zamansky

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa's approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved, da Costa's approach has led to the family of Logics of Formal (In)consistency (LFIs). In this paper we provide non-deterministic semantics for a very large family of first-order LFIs (which includes da Costa's original system C*₁, as well as thousands of other logics). We show that our semantics is effective and modular, and we use this effectiveness to derive some important properties of logics in this family.

Original language	English
Title of host publication	Algebraic and Proof-Theoretic Aspects of Non-classical Logics
Subtitle of host publication	Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday
Publisher	Springer Verlag
Pages	1-24
Number of pages	24
ISBN (Print)	3540759387, 9783540759386
DOIs	https://doi.org/10.1007/978-3-540-75939-3_1
State	Published - 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4460 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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10.1007/978-3-540-75939-3_1

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Avron, A., & Zamansky, A. (2007). Many-valued non-deterministic semantics for first-order logics of formal (In)consistency. In Algebraic and Proof-Theoretic Aspects of Non-classical Logics: Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday (pp. 1-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4460 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-540-75939-3_1

Avron, Arnon ; Zamansky, Anna. / Many-valued non-deterministic semantics for first-order logics of formal (In)consistency. Algebraic and Proof-Theoretic Aspects of Non-classical Logics: Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday. Springer Verlag, 2007. pp. 1-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa's approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved, da Costa's approach has led to the family of Logics of Formal (In)consistency (LFIs). In this paper we provide non-deterministic semantics for a very large family of first-order LFIs (which includes da Costa's original system C*1, as well as thousands of other logics). We show that our semantics is effective and modular, and we use this effectiveness to derive some important properties of logics in this family.",

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Avron, A & Zamansky, A 2007, Many-valued non-deterministic semantics for first-order logics of formal (In)consistency. in Algebraic and Proof-Theoretic Aspects of Non-classical Logics: Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4460 LNAI, Springer Verlag, pp. 1-24. https://doi.org/10.1007/978-3-540-75939-3_1

Many-valued non-deterministic semantics for first-order logics of formal (In)consistency. / Avron, Arnon; Zamansky, Anna.
Algebraic and Proof-Theoretic Aspects of Non-classical Logics: Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday. Springer Verlag, 2007. p. 1-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4460 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Avron A, Zamansky A. Many-valued non-deterministic semantics for first-order logics of formal (In)consistency. In Algebraic and Proof-Theoretic Aspects of Non-classical Logics: Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday. Springer Verlag. 2007. p. 1-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-75939-3_1

Many-valued non-deterministic semantics for first-order logics of formal (In)consistency

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