Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Logic programming and databases
Logic programming and databases
A fixpoint semantics for disjunctive logic programs
Journal of Logic Programming
Foundations of disjunctive logic programming
Foundations of disjunctive logic programming
Data & Knowledge Engineering
Extending the Smodels system with cardinality and weight constraints
Logic-based artificial intelligence
Relational Databases and Homogeneity in Logics with Counting
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
Relational databases and homogeneity in logics with counting
Acta Cybernetica
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We investigate cardinality constraints of the form M →Θ K, where M is a set and Θ is one of the comparison operators "=", "≤", or "≥"; such a constraint states that "exactly", "at most", or "at least", respectively, K elements out of the set M have to be chosen. We show how a set C of constraints can be represented by means of a positive-disjunctive deductive database PC, such that the models of PC correspond to the solutions of C. This allows for embedding cardinality constraints into applications dealing with incomplete knowledge. We also present a sound calculus represented by a definite logic program Pcc, which allows for directly reasoning with sets of exactly-cardinality constraints (i.e., where Θ is "="). Reasoning with Pcc is very efficient, and it can be used for performance reasons before PC is evaluated. For obtaining completeness, however, PC is necessary, since we show the theoretical result that a sound and complete calculus for exactly-cardinality constraints does not exist.