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Max-ASP: Maximum Satisfiability of Answer Set Programs

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Book cover Logic Programming and Nonmonotonic Reasoning (LPNMR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5753))

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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Author information

Authors and Affiliations

  1. Department of Information and Computer Science, Helsinki University of Technology TKK, PO Box 5400, FI, 02015, TKK, Finland

    Emilia Oikarinen & Matti Järvisalo

Authors
  1. Emilia Oikarinen
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  2. Matti Järvisalo
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Editor information

Editors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey

    Esra Erdem

  2. Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay,, Hong Kong

    Fangzhen Lin

  3. Institut für Informatik, Universität Potsdam, August-Bebel-Str. 89, D-14482, Potsdam, Germany

    Torsten Schaub

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© 2009 Springer-Verlag Berlin Heidelberg

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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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  • DOI: https://doi.org/10.1007/978-3-642-04238-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04237-9

  • Online ISBN: 978-3-642-04238-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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