Decidable reasoning in terminological knowledge representation systems

Abstract

Terminological Knowledge Representation Systems (TKRS) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRS. The new features studied, all of practical interest, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability-, subsumption- and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems and can be easily turned into a procedure using exponential space. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.