The Complexity of Concept Languages

Abstract

A basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called a concept language (or description logic), which is given a well-de ned set-theoretic semantics. The e ciency of reasoning has often been advocated as a primary motivation for the use of such systems. The main contributions of the paper are: (1) a complexity analysis of concept satis ability and subsumption for a wide class of concept languages; (2) the algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform. This is an extended and revised version of a paper presented at the 2nd Int. Conf. on Principles of Knowledge Representation and Reasoning, Cambridge, MA, 1991.

Abox Satisfiability Reduced to Terminological Reasoning in Expressive Description Logics

“…the size of the KB. 6 Therefore the size of a precompletion cannot exceed the number of individual names multiplied by the number of concept expressions, and this number is still polynomial w.r.t. the size of the KB.…”

“…The DL based design of these languages allows them to exploit both formal results (e.g., w.r.t. the decidability and complexity of key inference problems [6]) and implemented systems from DL research. Reasoning with Aboxes is likely to be of increasing importance, e.g., in Semantic Web applications, where it will be necessary not only to reason with concepts, but also with individuals (web resources) that instantiate them, and in particular to answer queries over sets of such individuals (e.g., see [7]).…”

Querying the Semantic Web: A Formal Approach

“…Several prominent web ontology languages, in particular OIL and DAML+OIL [11], are based on DLs; this allows them to exploit formal results (e.g., w.r.t. the decidability and complexity of key inference problems [8]) and algorithm designs from DL research, as well as to use DL based knowledge representation systems to provide reasoning support for web applications [14].…”

Learning Generalized Policies from Planning Examples Using Concept Languages

“…The notion of classes of objects is central in the languages developed in AI known as concept languages or description logics [8][9][10]. These languages have the expressive power of subsets of standard first-order logic but with a syntax that is suited for representing and reasoning with classes of objects.…”

“…First, it relies on background knowledge in the form of support predicates that express key features of the domain, and second, the resulting policies do not generalize so well. In this paper we aim to show that these weaknesses can be addressed by learning generalized policies expressed using a concept language [8][9][10][11]. Concept languages have the expressive power of fragments of standard first-order logic but with a syntax that is suited for representing and reasoning with classes of objects.…”