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On finitely-valued Fuzzy Description Logics

AuthorsCerami, Marco; García-Cerdaña, Àngel ; Esteva, Francesc
KeywordsT - Norm
Fuzzy description logic
Fuzzy logic of a finite t-norm
Description logic
Mathematical fuzzy logic
Issue Date2014
CitationInternational Journal of Approximate Reasoning 55: 1890- 1916 (2014)
Abstract© 2013 Elsevier Inc. This paper deals with finitely-valued fuzzy description languages from a logical point of view. From recent results in Mathematical Fuzzy Logic and following [44], we develop a Fuzzy Description Logic based on the fuzzy logic of a finite BL-chain. The constructors of the languages presented in this paper correspond to the connectives of that logic (containing an involutive negation, Monteiro-Baaz delta and hedges). The paper addresses the hierarchy of fuzzy attributive languages; knowledge bases and their reductions; reasoning tasks; and complexity. Our results regarding decidability together with a summary of the known results related to computational complexity are of particular interest. In Appendix B we also provide axiomatizations for expansions of the logic of a finite BL-chain considered in the paper.
Identifiersdoi: 10.1016/j.ijar.2013.09.021
issn: 0888-613X
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