Logic programs with monotone abstract constraint atoms

Victor W. Marek, Ilkka Niemelä, MirosŁaw Truszczyński

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageEnglish
Pages (from-to)167-199
Number of pages33
JournalTheory and Practice of Logic Programming
Issue number2
StatePublished - Mar 2008

Bibliographical note

Funding Information:
The authors wish to thank the anonymous reviewers for their detailed comments and suggestions, which helped improve the paper. The second author was supported by the Academy of Finland grant 211025. The other two authors were supported by the NSF grants IIS-0097278 and IIS-0325063.


  • Constraints
  • Logic programs
  • Stable models

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics
  • Artificial Intelligence


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