Weak and strong disjunction in possibilistic ASP

Bauters, Kim, Schockaert, Steven ORCID: https://orcid.org/0000-0002-9256-2881, De Cock, Martine and Vermeir, Dirk 2011. Weak and strong disjunction in possibilistic ASP. Presented at: SUM 2011: 5th International Conference on Scalable Uncertainty Management, Dayton, OH, USA, 10-13 October 2011. Published in: Benferhat, S. and Grant, J. eds. Scalable Uncertainty Management: 5th International Conference, SUM 2011, Dayton, OH, USA, October 10-13, 2011. Proceedings. Lecture Notes in Computer Science. Lecture Notes in Computer Science , vol.6929 Berlin and Heidelberg: Springer, pp. 475-488. 10.1007/978-3-642-23963-2_37

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Abstract

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.

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Publisher:	Springer
ISSN:	0302-9743
Last Modified:	25 Oct 2022 09:42
URI:	https://orca.cardiff.ac.uk/id/eprint/59689

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