Terminological logics with modal operators

Abstract

Terminological knowledge representation formalisms can be used to represent objective, time-independent facts about an application domain. Notions like belief, intentions, time - which are essential for the representation of multi-agent environments - can only be expressed in a very limited way. For such notions, modal logics with possible worlds semantics provides a formally well-founded and well-investigated basis. This paper presents a framework for integrating modal operators into terminological knowledge representation languages. These operators can be used both inside of concept expressions and in front of terminological and assertional axioms. The main restrictions are that all modal operators are interpreted in the basic logic K, and that we consider increasing domains instead of constant domains. We introduce syntax and semantics of the extended language, and show that satisfiability of finite sets of formulas is decidable.