关键词: 形式概念,上近似,下近似,粗糙集,描述逻辑

Abstract: The existing rough description logic(RDL) are all based on the classical rough set theory,i.e,when dealing with uncertainty knowledge,one must have an equivalence relation on the considered domain of objects in advance.In fact,people often encounter a case that there is a formal concept structure on the domain of objects.A natural question is how to deal with the possibly occurring uncertain concepts.We combined formal concept analysis and rough set theory to establish two new RDLs.The approach proposed by Y.Y.Yao in literature [14] is applied in the frameworks of the new RDLs,where the upper and lower approximations of a non-definable concept are defined by lattice-theoretical operators and set-theoretical operators respectively,and particularly,a new form of lower approximation which is diffe-rent from the previous form is defined.The notions are very different from the classical form,but it is pretty practical.Based on the novel notions of the upper and lower approximations,we added the approximation operators to the structure of description logic.Then two new RDLs FlALC and FsALC were established.The corresponding semantic and syntax were given.At last,we also gave an extended Tableaux algorithm.It can be used to solve some related reasoning problems.

Key words: Formal concept,Upper approximation,Lower approximations,Rough set,Description logic