Abstract
We investigate quantifier elimination of first order logic over fuzzy algebras. Fuzzy algebras are defined from continuous t-norms over the unit interval, and subsume Łukasiewicz [28, 29], Gödel [16, 12] and Product [19] Logic as most prominent examples. We show that a fuzzy algebra has quantifier elimination iff it is one of the abovementioned logics. Moreover, we show quantifier elimination for various extensions of these logics, and observe other model-theoretic properties of fuzzy algebras. Further considerations are devoted to approximation of fuzzy logics by finite-valued logics.
Cite
CITATION STYLE
Baaz, M., & Veith, H. (1999). Quantifier elimination in fuzzy logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1584, pp. 399–414). Springer Verlag. https://doi.org/10.1007/10703163_27
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
