Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
Foundations of deductive databases and logic programming
Signed data dependencies in logic programs
Journal of Logic Programming
Datalog extensions for database queries and updates
Journal of Computer and System Sciences
Journal of Computer and System Sciences
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Contributions to the Theory of Logic Programming
Journal of the ACM (JACM)
Negation and minimality in non-horn databases
PODS '93 Proceedings of the twelfth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Database research at AT&T Bell Laboratories
ACM SIGMOD Record
Structural totality and constraint stratification
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Perspectives on database theory
ACM SIGACT News
On kernels, defaults and even graphs
Annals of Mathematics and Artificial Intelligence
On odd and even cycles in normal logic programs
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Using ASP for knowledge management with user authorization
Data & Knowledge Engineering
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We address the question of when the structure of a Datalog program with negation guarantees the existence of a fixpoint. We propose a semantics of Datalog programs with negation, which we call the tie–breaking semantics. The tie–breaking semantics can be computed in polynomial time, and results in a fix-point whenever the rule–goal graph of the program has no cycle with an odd number of negative edges. We show that, in some well-defined sense, this is the most general fixpoint semantics of negation possible; in particular we show that if a cycle with an odd number of negative edges is present, then the logic program is not structurally total, that is, it has an alphabetic variant which has no fixpoint semantics whatsoever. Determining whether a program is (nonstructurally) total is undecidable.