Abstract
This paper studies answer set programming (ASP) in the generalized context of soft constraints and optimization criteria. In analogy to the well-known Max-SAT problem of maximum satisfiability of propositional formulas, we introduce the problems of unweighted and weighted Max-ASP. Given a normal logic program P, in Max-ASP the goal is to find so called optimal Max-ASP models, which minimize the total cost of unsatisfied rules in P and are at the same time answer sets for the set of satisfied rules in P. Inference rules for Max-ASP are developed, resulting in a complete branch-and-bound algorithm for finding optimal models for weighted Max-ASP instances. Differences between the Max-ASP problem and earlier proposed related concepts in the context of ASP are also discussed. Furthermore, translations between Max-ASP and Max-SAT are studied.
This work is financially supported by Academy of Finland under the project Methods for Constructing and Solving Large Constraint Models (grant #122399).
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Oikarinen, E., Järvisalo, M. (2009). Max-ASP: Maximum Satisfiability of Answer Set 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_21
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