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On Witnessed Models in Fuzzy Logic III - Witnessed Gödel Logics
- 1.0342154 - ÚI 2011 RIV DE eng J - Journal Article
Hájek, Petr
On Witnessed Models in Fuzzy Logic III - Witnessed Gödel Logics.
Mathematical Logic Quarterly. Roč. 56, č. 2 (2010), s. 171-174. ISSN 0942-5616. E-ISSN 1521-3870
R&D Projects: GA MŠMT(CZ) 1M0545
Institutional research plan: CEZ:AV0Z10300504
Keywords : mathematical fuzzy logic * Gödel logic * witnessed models * arithmetical complexity
Subject RIV: BA - General Mathematics
Impact factor: 0.361, year: 2010
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 Pi2-complete.
Permanent Link: http://hdl.handle.net/11104/0184967
Number of the records: 1