On strong maximality of paraconsistent finite-valued logics

Arnon Avron, Ofer Arieli, Anna Zamansky

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

Abstract

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain as much as possible from classical logic. In this paper we introduce a new, strong notion of maximal paraconsistency, which is based on possible extensions of the consequence relation of a logic. We investigate this notion in the framework of finite-valued paraconsistent logics, and show that for every n > 2there exists an extensive family of n-valued logics, each of which is maximally paraconsistent in our sense, is partial to classical logic, and is not equivalent to any k-valued logic with k < n. On the other hand, we specify a natural condition that guarantees that a paraconsistent logic is contained in a logic in the class of three-valued paraconsistent logics, and show that all reasonably expressive logics in this class are maximal.

Original languageEnglish
Title of host publicationProceedings - 25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages304-313
Number of pages10
ISBN (Print)9780769541143
DOIs
StatePublished - 2010
Event25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010 - Edinburgh, United Kingdom
Duration: 11 Jul 201014 Jul 2010

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871

Conference

Conference25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010
Country/TerritoryUnited Kingdom
CityEdinburgh
Period11/07/1014/07/10

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