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A Logical Approach to Interpolation Based on Similarity Relations

AuthorsDubois, Didier; Prade, Henri; Esteva, Francesc ; García-Calvés, Pere ; Godo, Lluis
KeywordsSimilarity logic
Graded consequence relations
Fuzzy similarity relations
Issue Date1997
CitationInternational Journal of Approximate Reasoning 17: 1- 36 (1997)
AbstractOne of the possible semantics of fuzzy sets is in terms of similarity; namely, a grade of membership of an item in a fuzzy set can be viewed as the degree of resemblance between this item and prototypes of the fuzzy set. In such a framework, an interesting question is how to devise a logic of similarity, where inference rules can account for the proximity between interpretations. The aim is to capture the notion of interpolation inside a logical setting. In this paper, we investigate how a logic of similarity dedicated to interpolation can be defined, by considering different natural consequence relations induced by the presence of a similarity relation on the set of interpretations. These consequence relations are axiomatically characterized in a way that parallels the characterization of nonmonotonic consequence relationships. It is shown how to reconstruct the similarity relation underlying a given family of consequence relations that obey the axioms. Our approach strikingly differs from the logics of indiscernibility, such as the rough-set logics, because emphasis is put on interpolation capabilities. Potential applications are fuzzy rule-based systems and fuzzy case-based reasoning, where notions of similarity play a crucial role. © 1997 Elsevier Science Inc.
Identifiersdoi: 10.1016/S0888-613X(96)00137-5
issn: 0888-613X
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