Semantical considerations on nonmonotonic logic
Artificial Intelligence
Logic programs with classical negation
Logic programming
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Logic Programming and Negation: A Survey.
Logic Programming and Negation: A Survey.
Annals of Mathematics and Artificial Intelligence
A Default Approach to Semantics of Logic Programs with Constraint Atoms
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Thirteen definitions of a stable model
Fields of logic and computation
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
Answer sets for propositional theories
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Well-supported semantics for description logic programs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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Answer set programming is the most appreciated framework for non-monotonic reasoning. Stable model semantics, as the semantics behind this success, has been subject to many extensions. The two main such extensions are equilibrium models and FLP semantics. Despite their very interesting foundations, they both have two problems: they cannot guarantee either minimality, or rationality of their intended models. That is, both these semantics allow models in which some atoms are self-justified (i.e., the only possible reason for including those atoms in the model are those atoms themselves). Present paper extends stable model semantics to the full propositional language while guaranteeing both properties above. Our extension is called supported because it guarantees the existence of noncircular justifications for all atoms in a supported model. These goals are achieved through a form of completion in intuitionistic logic. We also discuss how supported models relate to other semantics for non-monotonic reasoning such as equilibrium models. Finally, we discuss the complexity of reasoning about supported models and show that the complexity of brave/cautious reasoning in supported semantics remains as before, i.e., the rationality property comes for no additional cost.