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Fuzzy Horn logic II

Radim Bělohlávek & Vilém Vychodil

Archive for Mathematical Logic 45 (2):149-177 (2006)

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Mathematical fuzzy logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.details The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting. Download Export citation Bookmark 6 citations
Continuous fuzzy Horn logic.Vilém Vychodil - 2006 - Mathematical Logic Quarterly 52 (2):171-186.details The paper deals with fuzzy Horn logic which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w.r.t. semantics over the unit interval [0, 1] with left-continuous t-norm and a residuated implication, provided that only certain fuzzy sets of formulas are considered. The model classes of fuzzy structures of FHL are characterized by closure properties. We also give (...) Download Export citation Bookmark

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