Reasoning with minimal models: Efficient algorithms and applications

Rachel Ben-Eliyahu-Zohary, Luigi Palopoli

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Reasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive head-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way.

Original languageEnglish
Pages (from-to)421-449
Number of pages29
JournalArtificial Intelligence
Issue number2
StatePublished - 1 Jan 1997


  • Disjunctive databases
  • Disjunctive default logic
  • Disjunctive logic programs
  • Linear time algorithms
  • Minimal models
  • Stable model semantics

ASJC Scopus subject areas

  • Language and Linguistics
  • Linguistics and Language
  • Artificial Intelligence


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