On finitely-valued Fuzzy Description Logics

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.