Extended logic programs as autoepistemic theories
Proceedings of the second international workshop on Logic programming and non-monotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Can we enforce full compositionality in uncertainty calculi?
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Monotonic and Residuated Logic Programs
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Possibilistic uncertainty handling for answer set programming
Annals of Mathematics and Artificial Intelligence
Probabilistic reasoning with answer sets
Theory and Practice of Logic Programming
Pstable Semantics for Logic Programs with Possibilistic Ordered Disjunction
AI*IA '09: Proceedings of the XIth International Conference of the Italian Association for Artificial Intelligence Reggio Emilia on Emergent Perspectives in Artificial Intelligence
Semantics for possibilistic disjunctive programs
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Dealing with explicit preferences and uncertainty in answer set programming
Annals of Mathematics and Artificial Intelligence
International Journal of Approximate Reasoning
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Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.