Answer Sets in a Fuzzy Equilibrium Logic

  • Steven Schockaert
  • Jeroen Janssen
  • Dirk Vermeir
  • Martine De Cock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5837)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Steven Schockaert
    • 1
  • Jeroen Janssen
    • 2
  • Dirk Vermeir
    • 2
  • Martine De Cock
    • 1
    • 3
  1. 1.Dept. of Applied Mathematics and Computer ScienceGhent UniversityBelgium
  2. 2.Dept. of Computer ScienceVrije Universiteit BrusselBelgium
  3. 3.Institute of TechnologyUniversity of WashingtonTacomaUSA

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