×

zbMATH — the first resource for mathematics

On witnessed models in fuzzy logic. (English) Zbl 1110.03013
Summary: 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). A systematic theory of known fuzzy logics endowed with this semantics is developed with special attention paid to problems of arithmetical complexity of sets of tautologies and of satisfiable formulas.

MSC:
03B52 Fuzzy logic; logic of vagueness
03B50 Many-valued logic
03D35 Undecidability and degrees of sets of sentences
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Esteva, J. Logic Computation 13 pp 532– (2003)
[2] Metamathematics of Fuzzy Logic (Kluwer, 1998).
[3] Hájek, Studia Logica 68 pp 129– (2001)
[4] Fuzzy logic and arithmetical hierarchy IV. In: First-Order Logic Revised (V. Hendricks, F. Neuhaus, S. A. Pedersen, U. Scheffler, and H. Wansing, eds.), pp. 107–115 (Logos Verlag, 2004).
[5] Hájek, Soft Computing 9 pp 935– (2005)
[6] Hájek, Fuzzy Sets and Systems 154 pp 1– (2005)
[7] and , On theories and models in fuzzy predicate logics. To appear in the Journal of Symbolic Logic. · Zbl 1111.03030
[8] Kozlíková, Arch. Math. Logic 45 pp 569– (2006)
[9] and , Provability in product logic. To appear in Archive for Mathematical Logic. · Zbl 1121.03035
[10] Montagna, Studia Logica 68 pp 143– (2001)
[11] Montagna, Arch. Math. Logic 44 pp 97– (2005)
[12] Mostert, Annals Math. 65 pp 117– (1957)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.