On Fuzzy Description Logics

The antecedents of DL languages are Network-based structures carrying the intuition that, by exploiting the notion of hierarchical structure, one could gain in terms of both ease of representation the efficiency of reasoning The basic elements of the representation are characterized as unary predicates, denoting sets of individuals, and binary predicates, denoting relationships between individuals. Such a characterization does not capture the constraints of network-based structures with respect to logic. They did not require all the machinery of FOL, but could be regarded as fragments of it [Brachman and Levesque, 1985]. In addition, different features of the representation language would lead to different fragments of FOL. Important consequence: recognition that the typical forms of reasoning used in structure-based representations could be accomplished by specialized reasoning techniques, without necessarily requiring FOL theorem provers. Moreover, reasoning in different fragments of FOL leads to computational problems of differing complexity. To emphasize that the representation language was used to establish the basic terminology adopted in the modeled domain. The emphasis was on the set of concept-forming constructs admitted in the language. In more recent years, after attention was further moved towards the properties of the underlying logical systems, the term Description Logics became popular. Description Logics: The language Terminology Denote a hierarchical structure built to provide an intensional representation of the domain of interest. DL language Concepts are interpreted semantically as sets and in FOL as unary predicates Roles are interpreted as binary relations and in FOL as binary predicates the Description language is built from concepts and roles by means of constructors Different DLs depend on constructors (more or less expressive) Example: the language AL AL (= attributive language) introduced by [Schmidt-Schauß and Smolka, 1991] as a minimal language that is of practical interest. attributive language: a language to express, concisely, certain natural constructions that are commonly used to build other concepts from simpler ones.