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

Authors Jia-Huai You, John Morris, Yi Bi

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Jia-Huai You
John Morris
Yi Bi

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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)


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.
  • Well-founded semantics
  • description logic programs
  • aggregate logic programs
  • three-valued logic.


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