The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
Combining answer set programming with description logics for the Semantic Web
Artificial Intelligence
Rules and Ontologies for the Semantic Web
Reasoning Web
Answer sets for logic programs with arbitrary abstract constraint atoms
Journal of Artificial Intelligence Research
A uniform integration of higher-order reasoning and external evaluations in answer-set programming
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Reconciling description logics and rules
Journal of the ACM (JACM)
Loop formulas for description logic programs
Theory and Practice of Logic Programming
A Novel Combination of Answer Set Programming with Description Logics for the Semantic Web
IEEE Transactions on Knowledge and Data Engineering
Extending logic programs with description logic expressions for the semantic web
ISWC'11 Proceedings of the 10th international conference on The semantic web - Volume Part I
Well-Supported semantics for logic programs with generalized rules
Correct Reasoning
Semantic independence in DL-programs
RR'12 Proceedings of the 6th international conference on Web Reasoning and Rule Systems
Eliminating nonmonotonic DL-Atoms in description logic programs
RR'13 Proceedings of the 7th international conference on Web Reasoning and Rule Systems
Data repair of inconsistent DL-programs
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
A rational extension of stable model semantics to the full propositional language
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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[Fages, 1994] introduces the notion of well-supportedness as a key requirement for the semantics 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 paper, 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 positive literals in rule bodies. The second one defines strongly well-supported models that are free of circular justifications caused by either positive or negative literals. We then define two new answer set semantics for DL-programs and characterize them in terms of the weakly and strongly well-supported models, respectively. The first semantics 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 dlatoms. 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.