Answer Sets in a Fuzzy Equilibrium Logic

  • Authors:

  • Steven Schockaert;Jeroen Janssen;Dirk Vermeir;Martine Cock

  • Affiliations:

  • Dept. of Applied Mathematics and Computer Science, Ghent University, Belgium;Dept. of Computer Science, Vrije Universiteit Brussel, Belgium;Dept. of Computer Science, Vrije Universiteit Brussel, Belgium;Dept. of Applied Mathematics and Computer Science, Ghent University, Belgium and Institute of Technology, University of Washington, Tacoma, USA

  • Venue:
  • RR '09 Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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.