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Circumscription and Projection as Primitives of Logic Programming

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Abstract

KWe pursue a representation of logic programs as classical first-order sentences. Different semantics for logic programs can then be expressed by the way in which they are wrapped into - semantically defined - operators for circumscription and projection. (Projection is a generalization of second-order quantification.) We demonstrate this for the stable model semantics, Clark's completion and a three-valued semantics based on the Fitting operator. To represent the latter, we utilize the polarity sensitiveness of projection, in contrast to second-order quantification, and a variant of circumscription that allows to express predicate minimization in parallel with maximization. In accord with the aim of an integrated view on different logic-based representation techniques, the material is worked out on the basis of first-order logic with a Herbrand semantics.

BibTeX - Entry

@InProceedings{wernhard:LIPIcs:2010:2598,
  author =	{Christoph Wernhard},
  title =	{{Circumscription and Projection as Primitives of Logic Programming}},
  booktitle =	{Technical Communications of the 26th International Conference on Logic Programming},
  pages =	{202--211},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-17-0},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{7},
  editor =	{Manuel Hermenegildo and Torsten Schaub},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2598},
  URN =		{urn:nbn:de:0030-drops-25981},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.ICLP.2010.202},
  annote =	{Keywords: }
}

Seminar: Technical Communications of the 26th International Conference on Logic Programming
Issue date: 2010
Date of publication: 2010


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