On Witnessed Models in Fuzzy Logic III - Witnessed Gödel Logics

0342154 - ÚI 2011 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT(CZ) 1M0545
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: mathematical fuzzy logic * Gödel logic * witnessed models * arithmetical complexity
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.361, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0184967