Logic programs with monotone cardinality atoms

Victor W. Marek, Ilkka Niemelä, Miroslaw Truszczyński

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations


We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We demonstrate that the operational concept of the one-step provability operator generalizes to mca-programs, but the generalization involves nondeterminism. Our main results show that the formalism of mca-programs is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with cardinality atoms and 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
Title of host publicationLogic Programming and Nonmonotonic Reasoning
EditorsIlkka Niemela, Vladimir Lifschitz
Number of pages13
ISBN (Electronic)354020721X, 9783540207214
StatePublished - 2004
Event7th International Conference on Logic Programming and Nonmonotonic Reasoning , LPNMR 2004 - Fort Lauderdale, United States
Duration: Jan 6 2004Jan 8 2004

Publication series

NameLecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)
ISSN (Print)0302-9743


Conference7th International Conference on Logic Programming and Nonmonotonic Reasoning , LPNMR 2004
Country/TerritoryUnited States
CityFort Lauderdale

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2004.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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