Bisimilarity in Fuzzy Description Logics Under the Zadeh Semantics

Abstract

Fuzzy description logics (DLs) are extensions of DLs for dealing with imprecise and vague concepts. They found the logical basis for fuzzy ontologies, which are useful for practical applications. Bisimilarity is a natural notion of equivalence between individuals in DLs. In this paper, for the first time, we introduce the notion of bisimilarity in fuzzy DLs under the Zadeh semantics. It is defined using our notion of <inline-formula><tex-math notation= LaTeX >$p$</tex-math></inline-formula>-cut simulation between fuzzy interpretations. The considered logics are fuzzy DLs that extend the fuzzy version of the DL <inline-formula><tex-math notation= LaTeX >$\\mathcal {ALC}_{\\bf reg}$</tex-math></inline-formula> (a variant of propositional dynamic logic) with features among inverse roles, the universal role, qualified number restrictions, nominals, and local reflexivity of a role. We provide results on preservation of information by the mentioned simulations, conditional invariance of ABoxes and TBoxes by bisimilarity between witnessed interpretations, as well as the Hennessy–Milner property for fuzzy DLs under the Zadeh semantics.