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- Title
On witnessed models in fuzzy logic III – witnessed Gödel logics.
- Authors
Häjek, Petr
- Abstract
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 (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects
FUZZY logic; GODEL numbers; INFINITE integrals; ARITHMETIC functions; MATHEMATICAL analysis; MATHEMATICAL models
- Publication
Mathematical Logic Quarterly, 2010, Vol 56, Issue 2, p171
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.200810047