The retrieval problem in a concept language with number restrictions

Abstract

In this paper, we study the retrieval problem in $\mathcal{A}\mathcal{L}\mathcal{N}$, which is a tractable concept language with number restrictions. Following the approach proposed in [12], this work differs from the classical framework in two respects. First, the definition of answer has been extended in order to refer to elements whose existence may be deduced but have no explicit representation in the knowledge base. Therefore, our answers are also more informative than the classical ones. Second, the query-answering algorithm is syntax-directed rather than of the generate-and-test sort. Due to number restrictions, answers are possibly infinite sets but, since they are regular languages, they are described by regular expressions. The query-answering algorithm relies on a finite automaton, which can be seen as a preprocessing of the knowledge base, because it is built from its completion and does not depend on the query. Both a declarative and an operational semantics are described, and proved to be equivalent.