On the computational cost of disjunctive logic programming: Propositional case

  • Thomas Eiter
  • Georg Gottlob


This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of well-known semantics, as well as the complexity of deciding whether a propositional formula is satisfied by all models according to a given semantics. We concentrate on finite propositional disjunctive programs with as well as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is Σ 2 p -complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is Π 2 p -complete; analogous results are derived for the answer sets semantics of extended disjunctive logic programs. Besides, we generalize previously derived complexity results for the generalized closed world assumption and other more sophisticated variants of the closed world assumption. Furthermore, we use the close ties between the logic programming framework and other nonmonotonic formalisms to provide new complexity results for disjunctive default theories and disjunctive autoepistemic literal theories.


Model Semantic Integrity Constraint Propositional Formula Default Theory Disjunctive Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Georg Gottlob
    • 1
  1. 1.Christian Doppler Laboratory for Expert Systems, Institut für InformationssystemeTechnische Universität WienWienAustria

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