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Declarative and procedural semantics of fuzzy similarity based unification. (English) Zbl 1249.68264
Summary: We argue that for fuzzy unification, we need a procedural and declarative semantics (as opposed to the two-valued case, where the declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in the narrow sense. We base our semantics on a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of predicate calculus with equality. Rules are many valued implications and not Horn clauses. We prove soundness and completeness of the fuzzy similarity based unification.

68T37 Reasoning under uncertainty in the context of artificial intelligence
03B52 Fuzzy logic; logic of vagueness
68Q55 Semantics in the theory of computing
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