Definitorially complete description logics

Abstract

The Terminology Box (TBox) of a Description Logic (DL) knowledge base is used to define new concepts in terms of primitive concepts and relations. The topic of this paper is the effect of the available operations in a DL on the length and the syntactic shape of definitions in a Terminology Box. Defining new concepts can be done in two ways: (1) in an explicit syntactical manner as in NewConcept. = C, with C an expression in which NewConcept does not occur. Acyclic TBoxes only contain such axioms. (2) implicitly, by writing a set of general inclusion axiomsTwith the property that in any model ofT, the interpretation ofNewConcept is uniquely de-termined by the interpretation of the primitive concepts and relations. The explicit manner is preferred because its syntac-tic simplicity makes it immediately clear that NewConcept is