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. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Oikarinen, E., & Järvisalo, M. (2009). Max-ASP: Maximum satisfiability of answer set programs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5753 LNAI, pp. 236–249). https://doi.org/10.1007/978-3-642-04238-6_21
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