N-SHOQ(D): A nonmonotonic extension of description logic SHOQ(D)

Ontologies play a central role in the development of the semantic web, as they provide precise definitions of shared terms in web resources. One important web ontology language is DAML + OIL. It has a formal semantics and a reasoning support through a mapping to the expressive description logic SHOQ (D) with the addition of inverse roles. One shortcoming of the SHOQ (D) is that the incomplete knowledge frequently emerging in the practice cannot be expressed by SHOQ(D). In this paper, a nonmonotonic extension of the SHOQ (D), called N-SHOQ (D), is presented to allow for dealing with incomplete knowledge in the semantic web. The syntax and semantic of N-SHOQ (D) are defined and its properties are studied in detail. The N-SHOQ (D) forms a formal underpinning for the nonmonotonic extension of the DAML + OIL language.