Non-deterministic semantics for paraconsistent C-systems

Arnon Avron

doi:10.1007/11518655_53

Non-deterministic semantics for paraconsistent C-systems

Arnon Avron^*

^*Corresponding author for this work

School of Computer Science

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

5 Scopus citations

Abstract

We provide non-deterministic semantics for the 3 basic paraconsistent C-systems C (also known as bC), Ci, and Cia, as well as to all 9 extensions of them by one or two of the schemata (I) ¬(φ∧¬φ) ⊃ oφ and (e) φ ⊃ ¬¬φ. This includes da Costa's original C ₁ (which is equivalent to Cila). Our semantics is 3-valued for the systems without (I), and infinite-valued for the systems with it. We prove that these results cannot be improved: neither of the systems without (I) has either a finite characteristic ordinary matrix or a two-valued characteristic non-deterministic matrix, and neither of the systems with (I) has a finite characteristic non-deterministic matrix. Still, our semantics suffices for providing decision procedures for all the systems investigated.

Original language	English
Title of host publication	Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 8th European Conference, ECSQARU 2005, Proceedings
Publisher	Springer Verlag
Pages	625-637
Number of pages	13
ISBN (Print)	3540273263, 9783540273264
DOIs	https://doi.org/10.1007/11518655_53
State	Published - 2005
Event	8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005 - Barcelona, Spain Duration: 6 Jul 2005 → 8 Jul 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3571 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005
Country/Territory	Spain
City	Barcelona
Period	6/07/05 → 8/07/05

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10.1007/11518655_53

Cite this

Avron, A. (2005). Non-deterministic semantics for paraconsistent C-systems. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 8th European Conference, ECSQARU 2005, Proceedings (pp. 625-637). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3571 LNAI). Springer Verlag. https://doi.org/10.1007/11518655_53

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title = "Non-deterministic semantics for paraconsistent C-systems",

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Avron, A 2005, Non-deterministic semantics for paraconsistent C-systems. in Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 8th European Conference, ECSQARU 2005, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3571 LNAI, Springer Verlag, pp. 625-637, 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005, Barcelona, Spain, 6/07/05. https://doi.org/10.1007/11518655_53

Non-deterministic semantics for paraconsistent C-systems. / Avron, Arnon.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 8th European Conference, ECSQARU 2005, Proceedings. Springer Verlag, 2005. p. 625-637 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3571 LNAI).

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

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Avron A. Non-deterministic semantics for paraconsistent C-systems. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 8th European Conference, ECSQARU 2005, Proceedings. Springer Verlag. 2005. p. 625-637. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11518655_53

Non-deterministic semantics for paraconsistent C-systems

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