Reasoning with axioms: theory and practice

Abstract

When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively inexpressive logics, and it is essential to deal with such axioms in an ecient manner if implemented systems are to be effective in real applications. This is particularly relevant to Description Logics, where subsumption reasoning with respect to a terminology is a fundamental problem. Two optimisation techniques that have proved to be particularly eective in dealing with terminologies are lazy unfolding and absorption. In this paper we seek to improve our theoretical understanding of these important techniques. We define a formal framework that allows the techniques to be precisely described, establish conditions under which they can be safely applied, and prove that, provided these conditions are respected, subsumption testing algo...