Towards complete answers in concept languages

Abstract

In recent years, much attention has been given to conceptbased knowledge bases. In spite of the fact that there are several wellknown distinct problems, like consistency, coherence, subsumption, instantiation, realization and retrieval, they have been reduced to each other, whenever possible, in order to prove (in)tractability and (un)decidability results. Only for the first three problems, however, have efficient algorithms been studied. In particular, little attention has been given to the retrieval problem which computes the set of individuals that belong to a given concept in all models of the knowledge base.

Lenzerini and Schaerf studied the retrieval problem in [10, 11] and proposed using two concept languages: one for expressing the knowledge in the base and the other for making queries. However, their algorithm works by generate-and-test in the sense that it tests, for every individual i that occurs in the knowledge base, if a certain concept C(i) (built from those concepts of the knowledge base associated with i) subsumes a subconcept of the query. The authors show that their query-answering algorithm is complete and tractable.

Our paper describes a similar system, but differs from the work of Lenzerini and Schaerf in two important respects. First, our query-answering algorithm is syntax-directed rather than of the generate-and-test sort, hence more efficient. This point is important in connection with actual implementations of the system. Second, we can provide answers that may refer to individuals whose existence may be deduced but have no explicit representation in the knowledge base. Thus, our answers are more complete, hence more informative to the user. We prove that our algorithm is also complete and tractable.