Research On Description Logic Based On Extension Set

Description logic is a knowledge representation formalisms based on the object, to which people pay more and more particular attention among a number of formal methods represented by knowledge. Especially with the research of ontology and semantic Web rising, the description logic that is the base of ontology language and semantic web logic has been the research focus.According to the different demands of application fields, the knowledge to be described is a range of complex, requiring the description logic to be able to express all kinds of knowledge. However, the traditional description logic can only describe the static, certain knowledge, with finite expression ability, thus we need to go along the extension research. In order to endow the traditional description logic with the ability to not only express and infer the dynamic, fuzzy knowledge, but also describe the solving strategy of the contradiction problem to realize the share and reuse of strategy, in this paper the extension set and extension transformation in extenics are introduced as follows:First of all, since the traditional description logic can not describe fuzzy information and the fuzzy extension description logic is not suitable to describe the contradiction problem although it can describe fuzzy information, a description logic based on static extension set is proposed. The static extension set, instead of the classical set and fuzzy set, is used to be the set theory foundation of the description logic. Semantic explanations of domain concepts, relations and individuals are given, and the consistency checking algorithm Tableau of the traditional description logic assertion formula set is extended to implement the expansion of assertion formula set with positive or negative region dependent degree, thus the consistency of assertion formula set is decided.Secondly, since neither the traditional description logic nor the fuzzy description logic can provide strategy for the solving of contradiction problem by describing the quantitative change and qualitative change of matter, a new description logic based on the dynamic extension set is proposed, which is an extension of the description logic based on the static extension set. The syntax form is defined, and the dynamic extension set combined with the semantic explanation method of traditional description logic is used to give the semantic explanation of the described knowledge. The basic reasoning problem is researched, the consistency checking algorithm of the description logic based on static extension set is extended, and i.e. the extension transformation rule is added to generate the new consistency checking algorithm of the assertion formula set. The rationality of the new algorithm is proved detailed, including the proofs of reliability, terminability and decidability. The contradiction problem and how to find the strategy of solving contradiction problem are analyzed.Finally, to improve the ability of describing concept of the description logic based on dynamic extension set, the constructor-qualifying number restriction is added and the extensible description logic with qualifying number restrictions is proposed. The concept description, such as≥>kR.C,≤kR.C, is injected, and the semantic explanation is given according to the semantic explanation method of the dynamic extension set and the traditional description logic. The main research focus is the extension rules of assertion formula concerning the concept>kR.C,