Abstract:

The existing rough description logic (RDL) is based on the classical rough set theory. In fact, one often encounters 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. In the paper, based on a combination of the formal concept analysis and the rough set theory, we provide the notion of a definable concept. For an undefinable concept (a rough set), the upper and lower approximations of a rough set based on formal concept are also given. The notions are very different from their classical forms, but they are pretty practical. Based on the novel notions of the upper and lower approximations, we add the approximation operators to the structure of description logic. Then a new RDL is established. The corresponding semantic meaning and syntax are given. Finally, an extended Tableaux algorithm is given, which can be used to solve some related reasoning problems.

Key words: formal concept;upper and lower approximations;rough set;description logic (DL);Tableaux algorithm.