Semantics of Logic Programs withAggregatesDavid

We investigate the semantics of aggregates (count, sum, : : :) in logic programs with function symbols and negation. In particular we address the meaning of programs with recursion through aggregation. We extend the two most successful semantic approaches to the problem of recursion through negation, well founded models and stable models, to programs with aggregates. We examine previously deened classes of aggregate programs: aggregate stratiied, group stratiied, magical stratiied, monotonic and closed semi-ring programs and relate our semantics to those previously deened. The well-founded model gives a semantics to all programs containing aggregates, and agrees with two-valued models already deened for aggregate and group stratiied programs. Stable models give a meaning to many programs with aggregation, including all of the above classes, and captures all the models that have been previously deened. Further, there are programs not captured in any previously deened class where the unique stable model agrees with their \intuitive" semantics.