A dichotomy in the complexity of propositional circumscription

Lefteris M. Kirousis, Phokion G. Kolaitis

Research output: Contribution to journalArticlepeer-review


The inference problem for propositional circumscription is known to be highly intractable and, in fact, harder than the inference problem for classical propositional logic. More precisely, in its full generality this problem is II2P-complete, which means that it has the same inherent computational complexity as the satisfiability problem for quantified Boolean formulas with two alternations (universal-existential) of quantifiers. We use Schaefer's framework of generalized satisfiability problems to study the family of all restricted cases of the inference problem for propositional circumscription. Our main result yields a complete classification of the "truly hard" (II2P-complete) and the "easier" cases of this problem (reducible to the inference problem for classical propositional logic). Specifically, we establish a dichotomy theorem which asserts that each such restricted case either is II2P-complete or is in coNP. Morever, we provide efficiently checkable criteria that tell apart the "truly hard" cases from the "easier" ones.

Original languageEnglish (US)
Pages (from-to)71-80
Number of pages10
JournalProceedings - Symposium on Logic in Computer Science
StatePublished - 2001

ASJC Scopus subject areas

  • Software
  • General Mathematics


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