On interplay of quantifiers in Gödel-Dummett fuzzy logics
- 30 Downloads
Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of the considered logics.
Key words or phrasesGödel-Dummett fuzzy logics Kripke model prenexability inter-expressibility quantifiers
Mathematics Subject Classification (2000)03B20 03B52 03B55
Unable to display preview. Download preview PDF.
- 1.Baaz, M., Preining, N., Zach, R.: Characterization of the Axiomatizable Prenex Fragments of First-Order Gödel Logics. In: 33rd International Symposium on Multiple-valued Logic, May 16–19, 2003, pp 175–180, Tokyo, IEEE Computer Society Press, 2003Google Scholar
- 3.Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, 1998Google Scholar
- 5.Kleene, S.C.: Introduction to Metamathematics. D. van Nostrand, 1952Google Scholar
- 6.Kozlíková, B.: Sémantické metody v intuicionistické predikátové logice (Semantical Methods in Intuitionistic Predicate Logic). Master's thesis, Faculty of Arts, Charles University, Department of Logic (2004)Google Scholar
- 7.Preining, N.: Complete Recursive Axiomatizability of Gödel Logics. Ph.D. Thesis, Vienna University of Technology, Austria, 2003Google Scholar