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Aggregate Semantics for Propositional Answer Set Programs

机译：Aggregate Semantics for Propositional Answer Set Programs

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摘要

Answer set programming (ASP) emerged in the late 1990s as a paradigm for knowledge representationand reasoning. The attractiveness of ASP builds on an expressive high-level modelinglanguage along with the availability of powerful off-the-shelf solving systems. While the utilityof incorporating aggregate expressions in the modeling language has been realized almostsimultaneously with the inception of the first ASP solving systems, a general semantics of aggregatesand its efficient implementation have been long-standing challenges. Aggregates have beenproposed and widely used in database systems, and also in the deductive database languageDatalog, which is one of the main precursors of ASP. The use of aggregates was, however, stillrestricted in Datalog (by either disallowing recursion or only allowing monotone aggregates),while several ways to integrate unrestricted aggregates evolved in the context of ASP. In thissurvey, we pick up at this point of development by presenting and comparing the main aggregatesemantics that have been proposed for propositional ASP programs. We highlight crucialproperties such as computational complexity and expressive power, and outline the capabilitiesand limitations of different approaches by illustrative examples.

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