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Foundations of logic programming; (2nd extended ed.)
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
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Information Processing Letters
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
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PODS '93 Proceedings of the twelfth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Causal models of disjunctive logic programs
Proceedings of the eleventh international conference on Logic programming
Characterizations of the Stable Semantics by Partial Evaluation
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
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Proceedings of the 6th Conference on Automated Deduction
A Classification Theory Of Semantics Of Normal Logic Programs: I. Strong Properties
Fundamenta Informaticae
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
RW'13 Proceedings of the 9th international conference on Reasoning Web: semantic technologies for intelligent data access
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It is wellknown that Minker's semantics GCWA for positive disjunctive programs P, i.e. to decide if a literal is true in all minimal models of P is Π P 2-complete. This is in contrast to the same entailment problem for semantics of non-disjunctive programs such as STABLE and SUPPORTED (both are co-NP-complete) as well as M supp P and WFS (that are even polynomial). Recently, the idea of reducing disjunctive to non-disjunctive programs by using so called shift-operations was introduced independently by Bonatti, Dix/Gottlob/Marek, and Schaerf. In fact, Schaerf associated to each semantics SEM for normal programs a corresponding semantics Weak-SEM for disjunctive programs and asked for the properties of these weak semantics, in particular for the complexity of their entailment relations. While Schaerf concentrated on Weak-STABLE and Weak-SUPPORTED, we investigate the weak versions of Apt/Blair/Walker's stratified semantics M supp P and of Van Gelder/Ross/Schlipf's well-founded semantics WFS. We show that credulous entailment for both semantics is NP-complete (consequently, sceptical entailment is co-NP-complete). Thus, unlike GCWA, the complexity of these semantics belongs to the first level of the polynomial hierarchy. Note that, unlike Weak-WFS, the semantics Weak-M supp P is not always defined: testing consistency of Weak-M supp P is also NP-complete. We also show that Weak-WFS and Weak-M supp P are cumulative and rational and that., in addition, Weak-WFS satisfies some of the well-behaved principles introduced by Dix.