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Weak and strong disjunction in possibilistic ASP

Kim Bauters (UGent) , Steven Schockaert (UGent) , Martine De Cock (UGent) and Dirk Vermeir
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Bioinformatics: from nucleotids to networks (N2N)
Abstract
Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating cer- tainty 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 particu- lar, 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.
Keywords
possibility theory, logic programming, uncertainty

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Chicago
Bauters, Kim, Steven Schockaert, Martine De Cock, and Dirk Vermeir. 2011. “Weak and Strong Disjunction in Possibilistic ASP.” In Lecture Notes in Artificial Intelligence, ed. Salem Benferhat and John Grant, 6929:475–488. Berlin, Germany: Springer.
APA
Bauters, Kim, Schockaert, S., De Cock, M., & Vermeir, D. (2011). Weak and strong disjunction in possibilistic ASP. In S. Benferhat & J. Grant (Eds.), Lecture Notes in Artificial Intelligence (Vol. 6929, pp. 475–488). Presented at the 5th International conference on Scalable Uncertainty Management (SUM 2011), Berlin, Germany: Springer.
Vancouver
1.
Bauters K, Schockaert S, De Cock M, Vermeir D. Weak and strong disjunction in possibilistic ASP. In: Benferhat S, Grant J, editors. Lecture Notes in Artificial Intelligence. Berlin, Germany: Springer; 2011. p. 475–88.
MLA
Bauters, Kim, Steven Schockaert, Martine De Cock, et al. “Weak and Strong Disjunction in Possibilistic ASP.” Lecture Notes in Artificial Intelligence. Ed. Salem Benferhat & John Grant. Vol. 6929. Berlin, Germany: Springer, 2011. 475–488. Print.
@inproceedings{1984121,
  abstract     = {Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating cer- tainty 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 particu- lar, 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.},
  author       = {Bauters, Kim and Schockaert, Steven and De Cock, Martine and Vermeir, Dirk},
  booktitle    = {Lecture Notes in Artificial Intelligence},
  editor       = {Benferhat, Salem and Grant, John},
  isbn         = {9783642239632},
  issn         = {0302-9743},
  keyword      = {possibility theory,logic programming,uncertainty},
  language     = {eng},
  location     = {Dayton, OH, USA},
  pages        = {475--488},
  publisher    = {Springer},
  title        = {Weak and strong disjunction in possibilistic ASP},
  url          = {http://dx.doi.org/10.1007/978-3-642-23963-2\_37},
  volume       = {6929},
  year         = {2011},
}

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