Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles.

*(English)*Zbl 0742.68064
Artificial intelligence, IJCAI-91, Proc. 12th Int. Conf., Sydney/Australia 1991, 446-451 (1991).

[For the entire collection see Zbl 0741.68016.]

In previous works, the author has defined the small KL-ONE-based language, called \(FL_ 0\), which allows only concept conjunctions and value restrictions, and three types of semantics (least fixed-point, greatest fixed-point, and descriptive semantics). The present paper shows that the concept defining facilities of \(FL_ 0\) with cyclic definitions and greatest fixed-point semantics can also be obtained by replacing cycles with role definitions that involve union, composition, and transitive closure of roles. Augmenting the \(ALC\) language [M. Schmidt-Schauss and G. Smolka, Attributive concept descriptions with unions and complements, SEKI Report SR-88-21 (1988)] with a transitive closure operator for roles, the author obtained the new \(ALC_{reg}\) language which allows negation, conjunction and disjunction, value-restrictions and exists-in-restrictions of concepts, union, composition, and transitive closure of roles, but disallows cyclic concept definitions. As a consequence, in contrast to other terminological KR-systems which incorporate the transitive closure of roles, the author can specify in \(ALC_{reg}\) a sound and complete algorithm for concept subsumption.

In previous works, the author has defined the small KL-ONE-based language, called \(FL_ 0\), which allows only concept conjunctions and value restrictions, and three types of semantics (least fixed-point, greatest fixed-point, and descriptive semantics). The present paper shows that the concept defining facilities of \(FL_ 0\) with cyclic definitions and greatest fixed-point semantics can also be obtained by replacing cycles with role definitions that involve union, composition, and transitive closure of roles. Augmenting the \(ALC\) language [M. Schmidt-Schauss and G. Smolka, Attributive concept descriptions with unions and complements, SEKI Report SR-88-21 (1988)] with a transitive closure operator for roles, the author obtained the new \(ALC_{reg}\) language which allows negation, conjunction and disjunction, value-restrictions and exists-in-restrictions of concepts, union, composition, and transitive closure of roles, but disallows cyclic concept definitions. As a consequence, in contrast to other terminological KR-systems which incorporate the transitive closure of roles, the author can specify in \(ALC_{reg}\) a sound and complete algorithm for concept subsumption.

Reviewer: N.Curteanu (Iaşi)