Secure and optimal base contraction in graded Łukasiewicz logics

Pere Pardo*, Pilar Dellunde, Lluís Godo

*Corresponding author for this work

Research output: Chapter in BookChapterResearchpeer-review

Abstract

The operation of base contraction was successfully characterized for a very general class of logics using the notion of remainder sets. Nevertheless, in the general case, this notion is inadequate for revision, where it is replaced by maximal consistent subsets. A natural question is whether this latter notion allows for a definition of contraction-like operators and, in case it does, what differences there exist w.r.t. standard contraction. We make some steps towards this direction for the case of graded expansions of one of the most prominent fuzzy logics, Łukasiewicz logic. We characterize contraction operators with a fixed security-threshold ε>0; we prove soundness of (an optimal) ω-contraction operation, and a collapse theorem from ω- to some ε-contraction for finite theories.

Original languageEnglish
Title of host publicationFrontiers in Artificial Intelligence and Applications
PublisherIOS Press
Pages265-274
Number of pages10
Edition1
ISBN (Print)9781607500612
DOIs
Publication statusPublished - 2009

Publication series

NameFrontiers in Artificial Intelligence and Applications
Number1
Volume202
ISSN (Print)0922-6389

Keywords

  • Base contraction
  • Deduction theorem
  • Fuzzy logics
  • Łukasiewicz logic

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