Expressive fuzzy description logics over lattices

It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. In this paper we present a fuzzy description logics framework based on certainty lattices. Our main feature is that an assertion is not just true or false like in classical description logics, but certain to some degree, where the certainty value is taken from a certainty lattice. We extend the well known fuzzy description logic based on fuzzy set theory f-SHINf-SHIN to the fuzzy description logic based on certainty lattices theory L-SHINL-SHIN. The syntax, semantics and logical properties of the L-SHINL-SHIN are given, and a sound, complete and terminating tableaux algorithm for deciding fuzzy ABox consistency w.r.t. RBox for the L-SHINL-SHIN is presented. In this paper various extensions of fuzzy description logics over lattices are also discussed.