Automata-based Reasoning in Fuzzy Description Logics

Description logics (DLs) are a family of well-studied knowledge representation formalisms designed to express and reason with the conceptual knowledge of application domains in a clear and well-understood manner. They have been successfully applied for representing large application domains, most prominently from the biological and medical fields. In their classical form, DLs are not adequate for handling vague or imprecise knowledge, which is a common staple in bio-medical knowlege. To alleviate this problem, fuzzy extensions of DLs have been introduced. As a prototypical example, we consider here the smallest propositionally closed fuzzy DL, which we call ⊗-ALC. The fuzzy DL ⊗-ALC is based on concepts and roles, which are interpreted as (fuzzy) unary and binary relations, respectively. Given the disjoint sets NR, and NC of role, and concept names, respectively, ⊗-ALC concepts are built through the grammar rule