The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Journal of the ACM (JACM)
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Tabled evaluation with delaying for general logic programs
Journal of the ACM (JACM)
Characterizations of the Disjunctive Well-Founded Semantics: Confluent Calculi and Iterated GCWA
Journal of Automated Reasoning
WFS + Branch and Bound = Stable Models
IEEE Transactions on Knowledge and Data Engineering
Computing Well-founded Semantics Faster
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
Improving the Alternating Fixpoint: The Transformation Approach
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
XSB: A System for Effciently Computing WFS
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Consistent Data Integration in P2P Deductive Databases
SUM '07 Proceedings of the 1st international conference on Scalable Uncertainty Management
Satisfiability checking for PC(ID)
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)| × size(P)) steps, where size(P) denotes the total number of occurrences of atoms in a logic program P. This bound is achieved by an algorithm introduced by Van Gelder and known as the alternating-fixpoint algorithm. Improving on the alternating-fixpoint algorithm turned out to be difficult. In this paper we study extensions and modifications of the alternating-fixpoint approach. We then restrict our attention to the class of programs whose rules have no more than one positive occurrence of an atom in their bodies. For programs in that class we propose a new implementation of the alternating-fixpoint method in which false atoms are computed in a top-down fashion. We show that our algorithm is faster than other known algorithms and that for a wide class of programs it is linear and so, asymptotically optimal.