Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web

Abstract

Vagueness and imprecision abound in multimedia information processing and retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to fuzzy description logic programs under the answer set semantics. We generalize normal description logic programs (dl-programs) under the answer set semantics by fuzzy vagueness and imprecision. We define a canonical semantics of positive and stratified fuzzy dl-programs in terms of a unique least model and iterative least models, respectively. We then define the answer set semantics of general fuzzy dl-programs, and show in particular that all answer sets of a fuzzy dl-program are minimal models, and that the answer set semantics of positive and stratified fuzzy dl-programs coincides with their canonical least model and iterative least model semantics, respectively. Furthermore, we also provide a characterization of the canonical semantics of positive and stratified fuzzy dl-programs in terms of a fixpoint and an iterative fixpoint semantics, respectively.