Optimisation of Terminological Reasoning

The problem of computing concept subsumption relationships has been the subject of much research, and sound and complete algorithms are now known for a wide range of DLs (for example [9, 2, 7, 11]). However, in spite of the fundamental importance of terminologies in DLs, most of these algorithms deal only with the problem of deciding subsumption between two concepts (or, equivalently, concept satisfiability), without reference to a terminology (but see [4, 5, 8, 11]). By restricting the kinds of assertion that can appear in a terminology, concepts can be syntactically expanded so as to explicitly include all relevant terminolog-ical information. This procedure, called unfolding, has mostly been applied to less expressive DLs. With more expressive DLs, in particular those supporting universal roles, it is often possible to encapsulate an arbitrary terminology in a single concept. This technique can be used with satisfiability testing to ensure that the result is valid with respect to the assertions in the terminology, a procedure called internalisation. Although the above mentioned techniques suffice to demonstrate the theoretical adequacy of satisfiability decision procedures for terminological reasoning, experiments with implementations have shown that, for reasons of (lack of) efficiency, they are highly unsatisfactory as a practical methodology for reasoning with DL terminologies. Firstly, experiments with the Kris system have shown that integrating unfolding with the (tableaux) satisfiability algorithm (lazy unfolding) leads to a significant improvement in performance [1]. More recently , experiments with the FaCT system have shown that reasoning becomes hopelessly intractable when internalisation is used to deal with larger terminologies [10]. However, the FaCT system has also demonstrated that this problem can be dealt with (at least for realistic terminologies) by using a combination of lazy unfolding and internalisation, having first manipulated the terminology in order to minimise the number of assertions that must be dealt with by internal-isation (a technique called absorption). It should be noted that, although these techniques were discovered while developing DL systems, they are applicable to