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DOI: 10.4230/LIPIcs.ICLP.2012.235

Reconciling Well-Founded Semantics of DL-Programs and Aggregate Programs

Authors: Jia-Huai You, John Morris, and Yi Bi

Published in: LIPIcs, Volume 17, Technical Communications of the 28th International Conference on Logic Programming (ICLP'12) (2012)

Abstract

Logic programs with aggregates and description logic programs (dl-programs) are two recent extensions to logic programming. In this paper, we study the relationships between these two classes of logic programs, under the well-founded semantics. The main result is that, under a satisfaction-preserving mapping from dl-atoms to aggregates, the well-founded semantics of dl-programs by Eiter et al., coincides with the well-founded semantics of aggregate programs, defined by Pelov et al. as the least fixpoint of a 3-valued immediate consequence operator under the ultimate approximating aggregate. This result enables an alternative definition of the same well-founded semantics for aggregate programs, in terms of the first principle of unfounded sets. Furthermore, the result can be applied, in a uniform manner, to define the well-founded semantics for dl-programs with aggregates, which agrees with the existing semantics when either dl-atoms or aggregates are absent.

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Jia-Huai You, John Morris, and Yi Bi. Reconciling Well-Founded Semantics of DL-Programs and Aggregate Programs. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 17, pp. 235-246, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{you_et_al:LIPIcs.ICLP.2012.235,
  author =	{You, Jia-Huai and Morris, John and Bi, Yi},
  title =	{{Reconciling Well-Founded Semantics of DL-Programs and Aggregate Programs}},
  booktitle =	{Technical Communications of the 28th International Conference on Logic Programming (ICLP'12)},
  pages =	{235--246},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-43-9},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{17},
  editor =	{Dovier, Agostino and Santos Costa, V{\'\i}tor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2012.235},
  URN =		{urn:nbn:de:0030-drops-36258},
  doi =		{10.4230/LIPIcs.ICLP.2012.235},
  annote =	{Keywords: Well-founded semantics, description logic programs, aggregate logic programs, three-valued logic.}
}

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Reconciling Well-Founded Semantics of DL-Programs and Aggregate Programs

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