Abstract: Ontologies play a central role in the development of the semantic web, as they p rovide precise definitions of shared terms in web resources. One important web o ntology 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 knowledg e frequently emerging in the practice cannot be expressed by SHOQ(D). In this pa per, 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.