Well-supported semantics for description logic programs
Yi-Dong Shen · 2011
[Fages, 1994] introduces the notion of well-supportedness as a key requirement for the seman-tics of normal logic programs and characterizes the standard answer set semantics in terms of the well-supportedness condition. With the property of well-supportedness, answer sets are guaranteed to be free of circular justifications. In this pa-per, we extend Fages ’ work to description logic programs (or DL-programs). We introduce two forms of well-supportedness for DL-programs. The first one defines weakly well-supported models that are free of circular justifications caused by posi-tive literals in rule bodies. The second one de-fines strongly well-supported models that are free of circular justifications caused by either positive or negative literals. We then define two new an-swer set semantics for DL-programs and charac-terize them in terms of the weakly and strongly well-supported models, respectively. The first se-mantics is based on an extended Gelfond-Lifschitz transformation and defines weakly well-supported answer sets that are free of circular justifications for the class of DL-programs without negative dl-atoms. The second semantics defines strongly well-supported answer sets which are free of circular justifications for all DL-programs. We show that the existing answer set semantics for DL-programs, such as the weak answer set semantics, the strong answer set semantics, and the FLP-based answer set semantics, satisfy neither the weak nor the strong well-supportedness condition, even for DL-programs without negative dl-atoms. This explains why their answer sets incur circular justifications. 1