Abstract
We improve the formulations of loop formulas for weight constraint and aggregate programs by investigating the level mapping characterization of the semantics for these programs. First, we formulate a level mapping characterization of the stable model semantics for weight constraint programs, based on which we define loop formulas for these programs. This approach makes it possible to build loop formulas for programs with arbitrary weight constraints without introducing new atoms. Secondly, we further use level mapping to characterize the semantics and propose loop formulas for aggregate programs. The main result is that for aggregate programs not involving the inequality comparison operator, the dependency graphs can be built in polynomial time. This compares to the previously known exponential time method.
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Liu, G. (2009). Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Programs. In: Erdem, E., Lin, F., Schaub, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2009. Lecture Notes in Computer Science(), vol 5753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04238-6_40
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DOI: https://doi.org/10.1007/978-3-642-04238-6_40
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