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Answer Sets in a Fuzzy Equilibrium Logic

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Web Reasoning and Rule Systems (RR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5837))

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Abstract

Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications. As one of the most general “classical” approaches, answer sets of arbitrary propositional theories can be defined as models in the equilibrium logic of Pearce. Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems. In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic. We show that the resulting notion of answer set is compatible with existing definitions, when the syntactic restrictions of the corresponding approaches are met. We furthermore locate the complexity of the main reasoning tasks at the second level of the polynomial hierarchy. Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.

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Author information

Authors and Affiliations

  1. Dept. of Applied Mathematics and Computer Science, Ghent University, Belgium

    Steven Schockaert & Martine De Cock

  2. Dept. of Computer Science, Vrije Universiteit Brussel, Belgium

    Jeroen Janssen & Dirk Vermeir

  3. Institute of Technology, University of Washington, Tacoma, WA, USA

    Martine De Cock

Authors
  1. Steven Schockaert
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  2. Jeroen Janssen
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  3. Dirk Vermeir
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  4. Martine De Cock
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Editor information

Editors and Affiliations

  1. Digital Enterprise Research Institute (DERI), National University of Ireland, IDA Business Park, Lower Dangan, Galway, Ireland

    Axel Polleres

  2. Departamento de Informatica, FCT/UNL, Centre for Artificial Intelligence (CENTRIA), Quinta da Torre, 2829-516, Caparica, Portugal

    Terrance Swift

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Schockaert, S., Janssen, J., Vermeir, D., De Cock, M. (2009). Answer Sets in a Fuzzy Equilibrium Logic. In: Polleres, A., Swift, T. (eds) Web Reasoning and Rule Systems. RR 2009. Lecture Notes in Computer Science, vol 5837. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05082-4_10

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  • DOI: https://doi.org/10.1007/978-3-642-05082-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05081-7

  • Online ISBN: 978-3-642-05082-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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