Description Logics over Lattices

In the last decade a substantial amount of work has been carried out in the context of Description Logics (DLs). DLs are a logical reconstruction of the so-called framebased knowledge representation languages, with the aim of providing a simple wellestablished Tarski-style declarative semantics to capture the meaning of the most popular features of structured representation of knowledge. A main point is that DLs are considered as to be attractive logics in knowledge based applications as they are a good compromise between expressive power and computational complexity. Despite their growing popularity, relatively little work has been carried out in extending them to the management of uncertain and imprecise information. This is a well-known and important issue whenever the real world information to be represented is of imperfect nature. In DLs, the problem has attracted the attention of some researchers and some frameworks have been proposed, which differ in the underlying notion of uncertainty and imprecision: e.g. probability theory, possibility theory, metric spaces, many-valued and fuzzy theory. In this paper we extend DLs allowing to express that a sentence is not just true or false like in classical DLs, but certain to some degree, which is taken from a certainty lattice. The certainty degree dictates to what extend (how certain it is that) a sentence is true. The adopted approach is more general than the fuzzy logic