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Answer Sets in a Fuzzy Equilibrium Logic

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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.
Keywords
PROGRAMS, PROPOSITIONAL THEORIES

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Chicago
Schockaert, Steven, Jeroen Janssen, Dirk Vermeir, and Martine De Cock. 2009. “Answer Sets in a Fuzzy Equilibrium Logic.” In Lecture Notes in Computer Science, 5837:135–149. Berlin: Springer.
APA
Schockaert, S., Janssen, J., Vermeir, D., & De Cock, M. (2009). Answer Sets in a Fuzzy Equilibrium Logic. Lecture Notes in Computer Science (Vol. 5837, pp. 135–149). Presented at the Third International Conference, RR 2009, Berlin: Springer.
Vancouver
1.
Schockaert S, Janssen J, Vermeir D, De Cock M. Answer Sets in a Fuzzy Equilibrium Logic. Lecture Notes in Computer Science. Berlin: Springer; 2009. p. 135–49.
MLA
Schockaert, Steven, Jeroen Janssen, Dirk Vermeir, et al. “Answer Sets in a Fuzzy Equilibrium Logic.” Lecture Notes in Computer Science. Vol. 5837. Berlin: Springer, 2009. 135–149. Print.
@inproceedings{861391,
  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 {\textquotedblleft}classical{\textquotedblright} 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.},
  author       = {Schockaert, Steven and Janssen, Jeroen and Vermeir, Dirk and De Cock, Martine},
  booktitle    = {Lecture Notes in Computer Science},
  isbn         = {978-3-642-05081-7},
  issn         = {0302-9743},
  keyword      = {PROGRAMS,PROPOSITIONAL THEORIES},
  language     = {eng},
  location     = {Chantilly, VA, USA},
  pages        = {135--149},
  publisher    = {Springer},
  title        = {Answer Sets in a Fuzzy Equilibrium Logic},
  url          = {http://dx.doi.org/10.1007/978-3-642-05082-4\_10},
  volume       = {5837},
  year         = {2009},
}

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