Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
Handbook of theoretical computer science (vol. B)
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
Logic programming and knowledge representation-the A-prolog perspective
Artificial Intelligence
Extending and implementing the stable model semantics
Artificial Intelligence
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates
Proceedings of the 17th International Conference on Logic Programming
Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
ASSAT: computing answer sets of a logic program by SAT solvers
Eighteenth national conference on Artificial intelligence
Inference methods for a pseudo-boolean satisfiability solver
Eighteenth national conference on Artificial intelligence
Strong equivalence made easy: nested expressions and weight constraints
Theory and Practice of Logic Programming
Weight constraints as nested expressions
Theory and Practice of Logic Programming
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
Logic programs with monotone abstract constraint atoms*
Theory and Practice of Logic Programming
Integrating answer set programming and constraint logic programming
Annals of Mathematics and Artificial Intelligence
Answer sets for logic programs with arbitrary abstract constraint atoms
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
A Default Approach to Semantics of Logic Programs with Constraint Atoms
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Towards an Embedded Approach to Declarative Problem Solving in ASP
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Properties of programs with monotone and convex constraints
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
A generalized gelfond-lifschitz transformation for logic programs with abstract constraints
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Loop formulas for logic programs with arbitrary constraint atoms
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Properties and applications of programs with monotone and convex constraints
Journal of Artificial Intelligence Research
Answer sets for logic programs with arbitrary abstract constraint atoms
Journal of Artificial Intelligence Research
Characterizations of stable model semantics for logic programs with arbitrary constraint atoms
Theory and Practice of Logic Programming
Logic programs with abstract constraint atoms: The role of computations
Artificial Intelligence
Logic programs with abstract constraints: representaton, disjunction and complexities
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Logic programming for knowledge representation
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Logic programs with abstract constraint atoms: the role of computations
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Logic Programs
Fundamenta Informaticae
Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Logic Programs
Fundamenta Informaticae
The loop formula based semantics of description logic programs
Theoretical Computer Science
Unfounded sets and well-founded semantics of answer set programs with aggregates
Journal of Artificial Intelligence Research
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We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ X ∈ C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudo-boolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the one-step provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.