Relational queries computable in polynomial time
Information and Control
The magic of duplicates and aggregates
Proceedings of the sixteenth international conference on Very large databases
Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Low complexity aggregation in GraphLog and Datalog
ICDT '90 Proceedings of the third international conference on database theory on Database theory
Minimum and maximum predicates in logic programming
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
The valid model semantics for logic programs
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Monotonic aggregation in deductive databases
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Constraint query languages (preliminary report)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Aggregation and Relevance in Deductive Databases
VLDB '91 Proceedings of the 17th International Conference on Very Large Data Bases
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
The valid model semantics for logic programs
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Monotonic aggregation in deductive databases
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Perspectives on database theory
ACM SIGACT News
Variable independence and aggregation closure
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Logics with aggregate operators
Journal of the ACM (JACM)
Dynamic Programming in Datalog with Aggregates
IEEE Transactions on Knowledge and Data Engineering
Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates
Proceedings of the 17th International Conference on Logic Programming
FoIKS '00 Proceedings of the First International Symposium on Foundations of Information and Knowledge Systems
Semantics of Partial-Order Programs
JELIA '98 Proceedings of the European Workshop on Logics in Artificial Intelligence
Variable Independence in Constraint Databases
IEEE Transactions on Knowledge and Data Engineering
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
Answer sets for logic programs with arbitrary abstract constraint atoms
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Answer sets for logic programs with arbitrary abstract constraint atoms
Journal of Artificial Intelligence Research
Declarative and computational properties of logic programs with aggregates
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Unfounded sets and well-founded semantics of answer set programs with aggregates
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
Common aggregation predicates have natural definitions in logic, either as first order sentences (min, max, etc.), or with elementary induction over a data structure that represents the relation (sum, count, etc.). The well-founded semantics for logic programs provides an interpretation of such definitions. The interpretation of first-order aggregates seems to be quite natural and intuitively satisfying, even in the presence of recursion through aggregation. Care is needed to get useful results on inductive aggregates, however. A basic building block is the “subset” predicate, which states that a data structure represents a subset of an IDB predicate, and which is definable in the well-founded semantics. The analogous “superset” is also definable, and their combination yields a “generic” form of findall. Surprisingly, findall must be used negatively to obtain useful approximations when the exact relation is not yet known.Extensions to the semantics, restrictions on the input, and other supplementary requirements proposed in earlier studies appear to be unnecessary for the purpose of attaching a meaning to a program that involves recursion through aggregation. For example, any reasonable definition of “shortest paths” tolerates negative weight edges, correctly computes shortest paths that exist, and leave tuples undefined where negative-weight cycles cause the shortest path not to exist. Other examples exhibit similarly robust behavior, when defined carefully. Connections with the generic model of computation are discussed briefly.