Semantics of logic programs with aggregates

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 defined classes of aggregate programs: aggregate stratified, group stratified, magical stratified, monotonic and closed semi-ring programs and relate our semantics to those previously defined. The well-founded model gives a semantics to all programs containing aggregates, and agrees with two-valued models already defined for aggregate and group stratified 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 defined. Further, there are programs not captured in any previously defined class where the unique stable model agrees with their ``intuitive'' semantics.