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On witnessed models in fuzzy logic III – witnessed Gödel logics

✍ Scribed by Petr Häjek

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 96 KB
Volume: 56
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810047

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✦ Synopsis

Gödel (fuzzy) logics with truth sets being countable closed subsets of the unit real interval containing 0 and 1 are studied under their usual semantics and under the witnessed semantics, the latter admitting only models in which the truth value of each universally quantified formula is the minimum of truth values of its instances and dually for existential quantification and maximum. An infinite system of such truth sets is constructed such that under the usual semantics the corresponding logics have pairwise different sets of (standard) tautologies, all these sets being non-arithmetical, whereas under the witnessed semantics all the logics have the same set of tautologies and it is Π2-complete. Further similar results are obtained.

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On witnessed models in fuzzy logic

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## Abstract Witnessed models of fuzzy predicate logic are models in which each quantified formula is witnessed, i.e. the truth value of a universally quantified formula is the minimum of the values of its instances and similarly for existential quantification (maximum). Systematic theory of known f

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