First-Order Semantics of Aggregates in Answer Set Programming Via Modified Circumscription
Michael Bartholomew, Joohyung Lee, Yunsong Meng · National Conference on Artificial Intelligence · 2011
We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczynski. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to first-order formulas containing aggregate expressions. Similar to the first-order stable model semantics by Ferraris, Lee and Lifschitz, the reformulations presented here are based on syntactic transformations that are similar to circumscription. The reformulations provide useful insights into the FLP semantics and its relationship to circumscription and the first-order stable model semantics.