. . . . "G\u00F6del (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."@en . "000276729000007" . "P(1M0545), Z(AV0Z10300504)" . "276959" . . . . "4"^^ . "mathematical fuzzy logic; G\u00F6del logic; witnessed models; arithmetical complexity"@en . "0942-5616" . "G\u00F6del (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." . "H\u00E1jek, Petr" . . . . "[B4CC0D5134FF]" . "RIV/67985807:_____/10:00342154!RIV11-MSM-67985807" . . "1"^^ . . "On Witnessed Models in Fuzzy Logic III - Witnessed G\u00F6del Logics" . "On Witnessed Models in Fuzzy Logic III - Witnessed G\u00F6del Logics" . . "DE - Spolkov\u00E1 republika N\u011Bmecko" . "Mathematical Logic Quarterly" . "1"^^ . "On Witnessed Models in Fuzzy Logic III - Witnessed G\u00F6del Logics"@en . "2" . . "56" . "On Witnessed Models in Fuzzy Logic III - Witnessed G\u00F6del Logics"@en . "RIV/67985807:_____/10:00342154" . . . . .