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

Abstract

There are numerous semantic web applications where dealing with vagueness and imprecision plays an important role. Some examples of such applications are (i) multimedia information processing and retrieval, (ii) natural language interfaces to the Web, and (iii) ontology mapping and information retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to normal fuzzy description logic programs under the answer set semantics, which are a generalization of normal description logic programs (dl-programs) under the answer set semantics by fuzzy vagueness and imprecision in both the description logic and the logic program component. 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. 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. Furthermore, we provide a reduction of fuzzy dl-programs under the answer set semantics to normal dl-programs under the answer set semantics. Finally, we also describe a special case of fuzzy dl-programs where query processing can be done in polynomial time in the data complexity.