Maximally paraconsistent three-valued logics

Ofer Arieli, Arnon Avron, Anna Zamansky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 SRM 3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives.

Original languageEnglish
Title of host publicationPrinciples of Knowledge Representation and Reasoning
Subtitle of host publicationProceedings of the 12th International Conference, KR 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages9
ISBN (Print)9781577354512
StatePublished - 2010
Externally publishedYes
Event12th International Conference on Principles of Knowledge Representation and Reasoning, KR 2010 - Toronto, ON, Canada
Duration: 9 May 201013 May 2010

Publication series

NameProceedings of the International Conference on Knowledge Representation and Reasoning
ISSN (Print)2334-1025
ISSN (Electronic)2334-1033


Conference12th International Conference on Principles of Knowledge Representation and Reasoning, KR 2010
CityToronto, ON

ASJC Scopus subject areas

  • Logic


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