Data functions, datalog and negation
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Logic programming and databases
Logic programming and databases
The magic of duplicates and aggregates
Proceedings of the sixteenth international conference on Very large databases
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 well-founded semantics of aggregation
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Modular stratification and magic sets for DATALOG programs with negation
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
The well-founded semantics of aggregation
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Shortest path by approximation in logic programs
ACM Letters on Programming Languages and Systems (LOPLAS)
LogicBase: a deductive database system prototype
CIKM '94 Proceedings of the third international conference on Information and knowledge management
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
Optimization and relaxation in constraint logic languages
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Logics with aggregate operators
Journal of the ACM (JACM)
Efficient Recursive Aggregation and Negation in Deductive Databases
IEEE Transactions on Knowledge and Data Engineering
Dynamic Programming in Datalog with Aggregates
IEEE Transactions on Knowledge and Data Engineering
FoIKS '00 Proceedings of the First International Symposium on Foundations of Information and Knowledge Systems
Variable Independence in Constraint Databases
IEEE Transactions on Knowledge and Data Engineering
Theory and Practice of Logic Programming
Compiling Comp Ling: practical weighted dynamic programming and the Dyna language
HLT '05 Proceedings of the conference on Human Language Technology and Empirical Methods in Natural Language Processing
Dyna: extending datalog for modern AI
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Logic and lattices for distributed programming
Proceedings of the Third ACM Symposium on Cloud Computing
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We propose a semantics for aggregates in deductive databases based on a notion of minimality. Unlike some previous approaches, we form a minimal model of a program component including aggregate operators, rather than insisting that the aggregate apply to atoms that have been fully determined, or that aggregate functions are rewritten in terms of negation. In order to guarantee the existence of such a minimal model we need to insist that the domains over which we are aggregating are complete lattices, and that the program is in a sense monotonic. Our approach generalizes previous approaches based on the well-founded semantics and various forms of stratification. We are also able to handle a large variety of monotonic (or pseudo-monotonic) aggregate functions.