The loop formula based semantics of description logic programs

Description logic programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored and we compare the canonical answer set semantics with the FLP-semantics and the answer set semantics by translating dl-programs into logic programs with abstract constraints. We present a clear picture on the relationship among these semantics variations for dl-programs.