A scheme for integrating concrete domains into concept languages.

*(English)*Zbl 0742.68063
Artificial intelligence, IJCAI-91, Proc. 12th Int. Conf., Sydney/Australia 1991, 452-457 (1991).

[For the entire collection see Zbl 0741.68016.]

In many applications, one would like to be able to refer to concrete domains, and predicates on these domains, naturally integrated into a concept language based on the KL-ONE representation language. The present paper proposes a scheme for integrating such concrete domains into a KL- ONE based knowledge representation and reasoning system. The authors begin by formally defining the notion of a concrete domain, and describing their scheme for extending a concept language by an arbitrary concrete domain. Taking as concept language the ALC language [M. Schmidt-Schauss and G. Smolka, Artif. Intell. 48(1), 1-26 (1991; Zbl 0712.68095)], the terminological and assertional parts are extended with the concrete domain, and integrated with the help of a unified model-theoretic semantics. The important inference problems such as subsumption, instantiation, and consistency are analyzed, just so the basic reasoning algorithm creating subtasks which have to be solved by the special purpose reasoner of the concrete domain. The basic reasoning algorithm is sound and complete, despite its PSPACE computational complexity in the worst case (but its behaviour is much better for typical knowledge bases). The motivation of the approach is to represent a mechanical engineering concept language extended to real arithmetics as its concrete domain.

In many applications, one would like to be able to refer to concrete domains, and predicates on these domains, naturally integrated into a concept language based on the KL-ONE representation language. The present paper proposes a scheme for integrating such concrete domains into a KL- ONE based knowledge representation and reasoning system. The authors begin by formally defining the notion of a concrete domain, and describing their scheme for extending a concept language by an arbitrary concrete domain. Taking as concept language the ALC language [M. Schmidt-Schauss and G. Smolka, Artif. Intell. 48(1), 1-26 (1991; Zbl 0712.68095)], the terminological and assertional parts are extended with the concrete domain, and integrated with the help of a unified model-theoretic semantics. The important inference problems such as subsumption, instantiation, and consistency are analyzed, just so the basic reasoning algorithm creating subtasks which have to be solved by the special purpose reasoner of the concrete domain. The basic reasoning algorithm is sound and complete, despite its PSPACE computational complexity in the worst case (but its behaviour is much better for typical knowledge bases). The motivation of the approach is to represent a mechanical engineering concept language extended to real arithmetics as its concrete domain.

Reviewer: N.Curteanu (Iaşi)

##### MSC:

68T30 | Knowledge representation |

68T27 | Logic in artificial intelligence |

03B65 | Logic of natural languages |

68T50 | Natural language processing |