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DOI: 10.4230/OASIcs.ICLP.2016.6

Justifications and Blocking Sets in a Rule-Based Answer Set Computation

Authors: Christopher Béatrix, Claire Lefèvre, Laurent Garcia, and Igor Stéphan

Published in: OASIcs, Volume 52, Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016)

Abstract

Notions of justifications for logic programs under answer set semantics have been recently studied for atom-based approaches or argumentation approaches. The paper addresses the question in a rule-based answer set computation: the search algorithm does not guess on the truth or falsity of an atom but on the application or non application of a non monotonic rule. In this view, justifications are sets of ground rules with particular properties. Properties of these justifications are established; in particular the notion of blocking set (a reason incompatible with an answer set) is defined, that permits to explain computation failures. Backjumping, learning, debugging and explanations are possible applications.

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Christopher Béatrix, Claire Lefèvre, Laurent Garcia, and Igor Stéphan. Justifications and Blocking Sets in a Rule-Based Answer Set Computation. In Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016). Open Access Series in Informatics (OASIcs), Volume 52, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{beatrix_et_al:OASIcs.ICLP.2016.6,
  author =	{B\'{e}atrix, Christopher and Lef\`{e}vre, Claire and Garcia, Laurent and St\'{e}phan, Igor},
  title =	{{Justifications and Blocking Sets in a Rule-Based Answer Set Computation}},
  booktitle =	{Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016)},
  pages =	{6:1--6:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-007-1},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{52},
  editor =	{Carro, Manuel and King, Andy and Saeedloei, Neda and De Vos, Marina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2016.6},
  URN =		{urn:nbn:de:0030-drops-67310},
  doi =		{10.4230/OASIcs.ICLP.2016.6},
  annote =	{Keywords: Answer Set Programming, Justification, Rule-based Computation}
}

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DOI: 10.4230/DagSemProc.05171.6

Possibilistic Stable Models

Authors: Pascal Nicolas, Laurent Garcia, and Igor Stéphan

Published in: Dagstuhl Seminar Proceedings, Volume 5171, Nonmonotonic Reasoning, Answer Set Programming and Constraints (2005)

Abstract

We present the main lines of a new framework that we have defined in order to improve the knowledge representation power of Answer Set Programming paradigm. Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity measure, on each rule of a normal logic program. First of all, we introduce possibilistic definite logic programs and show how to compute the conclusions of such programs both in syntactic and semantic ways. The syntactic handling is done by help of a fix-point operator, the semantic part relies on a possibility distribution on all sets of atoms and the two approaches are shown to be equivalent. In a second part, we define what is a possibilistic stable model for a normal logic program, with default negation. Again, we define a possibility distribution allowing to determine the stable models. We end our presentation by showing how we can use our framework to adressing inconsistency in Answer Set Programming.

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Pascal Nicolas, Laurent Garcia, and Igor Stéphan. Possibilistic Stable Models. In Nonmonotonic Reasoning, Answer Set Programming and Constraints. Dagstuhl Seminar Proceedings, Volume 5171, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{nicolas_et_al:DagSemProc.05171.6,
  author =	{Nicolas, Pascal and Garcia, Laurent and St\'{e}phan, Igor},
  title =	{{Possibilistic Stable Models}},
  booktitle =	{Nonmonotonic Reasoning, Answer Set Programming and Constraints},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5171},
  editor =	{Gerhard Brewka and Ilkka Niemel\"{a} and Torsten Schaub and Miroslaw Truszczynski},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05171.6},
  URN =		{urn:nbn:de:0030-drops-2641},
  doi =		{10.4230/DagSemProc.05171.6},
  annote =	{Keywords: Non monotonic reasoning, uncertainty, possibility theory}
}

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Justifications and Blocking Sets in a Rule-Based Answer Set Computation

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Possibilistic Stable Models

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