Logic programs with monotone abstract constraint atoms*

  • Authors:

  • Victor w. Marek;Ilkka NiemelÄ;MirosŁaw TruszczyŃski

  • Affiliations:

  • Department of computer science, university of kentucky, lexington, ky 40506, usa (e-mail: marek@cs.uky.edu);Department of computer science and engineering, helsinki university of technology, p.o. box 5400, fi-02015 tkk, finland (e-mail: ilkka.niemela@tkk.fi);Department of computer science, university of kentucky, lexington, ky 40506, usa (e-mail: mirek@cs.uky.edu)

  • Venue:
  • Theory and Practice of Logic Programming
  • Year:
  • 2008

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Abstract

We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the generalization involves nondeterminism. Our main results demonstrate that our formalism is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with weight atoms lparse programs) with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.