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Answer Set Programming (ASP) emerged in the late 1990ies as a paradigm forKnowledge Representation and Reasoning. The attractiveness of ASP builds on anexpressive high-level modeling language along with the availability of powerfuloff-the-shelf solving systems. While the utility of incorporating aggregateexpressions in the modeling language has been realized almost simultaneouslywith the inception of the first ASP solving systems, a general semantics ofaggregates and its efficient implementation have been long-standing challenges.Aggregates have been proposed and widely used in database systems, and also inthe deductive database language Datalog, which is one of the main precursors ofASP. The use of aggregates was, however, still restricted in Datalog (by eitherdisallowing recursion or only allowing monotone aggregates), while several waysto integrate unrestricted aggregates evolved in the context of ASP. In thissurvey, we pick up at this point of development by presenting and comparing themain aggregate semantics that have been proposed for propositional ASPprograms. We highlight crucial properties such as computational complexity andexpressive power, and outline the capabilities and limitations of differentapproaches by illustrative examples.

Aggregate Semantics for Propositional Answer Set Programs