Reasoning with rough description logics: An approximate concepts approach

The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in description logics are analyzed in this paper. Approximate concepts are introduced to description logics based on rough set theory, and a kind of new rough description logic RDLACRDLAC (rough description logic based on approximate concepts) is proposed based on approximate concepts. The syntax, semantics and properties of the RDLACRDLAC are given. It is proved that the approximate concept satisfiability (definitely satisfiability and possibly satisfiability) reasoning problem and approximate concepts rough subsumption reasoning problem w.r.t. rough TBox in RDLACRDLAC may be reduced to the concept satisfiability reasoning problem in (almost) standard ALC (the description logic that provides the Boolean concept constructors plus the existential and universal restriction constructors). The works of this paper provide logic foundations for approximate ontologies and theoretical foundations for reasoning algorithms of more expressive rough description logics including approximate concepts, number restrictions, nominals, inverse roles and role hierarchies.