On Finitely Valued Fuzzy Description Logics: The Łukasiewicz Case

Following the guidelines proposed by Hájek in [1], some proposals of research on Fuzzy Description Logics (FDLs) were given in [2]. One of them consists in the definition and development of a family of description languages, each one having as underlying fuzzy logic the expansion with an involutive negation and truth constants of the logic defined by a divisible finite t-norm. A general framework for finitely valued FDLs was presented in [3]. In the present paper we study the family of languages ALC Ln based on the finitely valued Lukasiewicz logics with truth constants. In addition, we provide an interpretation of these FDLs into fuzzy multi-modal systems. We also deal with the corresponding reasoning tasks and their relationships, and we report some results on decidability and computational complexity.