Bilattices and the semantics of logic programming
Journal of Logic Programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
The well-founded semantics of aggregation
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Low-complexity aggregation in GraphLog and Datalog
ICDT Selected papers of the 4th international conference on Database theory
Extending the well-founded and valid semantics for aggregation
ILPS '93 Proceedings of the 1993 international symposium on Logic programming
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
The Magic of Duplicates and Aggregates
VLDB '90 Proceedings of the 16th International Conference on Very Large Data Bases
The Well-Founded Semantics Is the Principle of Inductive Definition
JELIA '98 Proceedings of the European Workshop on Logics in Artificial Intelligence
Stable Model Semantics of Weight Constraint Rules
LPNMR '99 Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning
Extending Classical Logic with Inductive Definitions
CL '00 Proceedings of the First International Conference on Computational Logic
Ultimate approximation and its application in nonmonotonic knowledge representation systems
Information and Computation
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
Logic programs with abstract constraint atoms
AAAI'04 Proceedings of the 19th national conference on Artifical 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
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
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
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Declarative and computational properties of logic programs with aggregates
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Annals of Mathematics and Artificial Intelligence
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
A 25-year perspective on logic programming
Logic programs with propositional connectives and aggregates
ACM Transactions on Computational Logic (TOCL)
ASP at work: spin-off and applications of the DLV system
Logic programming, knowledge representation, and nonmonotonic reasoning
Dynamic magic sets for programs with monotone recursive aggregates
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
Unfounded sets for disjunctive logic programs with arbitrary aggregates
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
LP with flexible grouping and aggregates using modes
LOPSTR'09 Proceedings of the 19th international conference on Logic-Based Program Synthesis and Transformation
Unfounded sets and well-founded semantics of answer set programs with aggregates
Journal of Artificial Intelligence Research
A top-k query answering procedure for fuzzy logic programming
Fuzzy Sets and Systems
Fundamenta Informaticae - Logic, Language, Information and Computation
RW'13 Proceedings of the 9th international conference on Reasoning Web: semantic technologies for intelligent data access
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In this paper, we propose an extension of the well-founded and stable model semantics for logic programs with aggregates. Our approach uses Approximation Theory, a fixpoint theory of stable and well-founded fixpoints of non-monotone operators in a complete lattice. We define the syntax of logic programs with aggregates and define the immediate consequence operator of such programs. We investigate the well-founded and stable semantics generated by Approximation Theory. We show that our approach extends logic programs with stratified aggregation and that it correctly deals with well-known benchmark problems such as the shortest path program and the company control problem.