### Answer Sets in a Fuzzy Equilibrium Logic

(2009) Lecture Notes in Computer Science. 5837. p.135-149- 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.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-861391

- author
- Steven Schockaert UGent, Jeroen Janssen UGent, Dirk Vermeir and Martine De Cock UGent
- organization
- year
- 2009
- type
- conference
- publication status
- published
- keyword
- PROGRAMS, PROPOSITIONAL THEORIES
- in
- Lecture Notes in Computer Science
- Lect. notes comput. sci.
- volume
- 5837
- issue title
- Web Reasoning and Rule Systems
- pages
- 135 - 149
- publisher
- Springer
- place of publication
- Berlin
- conference name
- Third International Conference, RR 2009
- conference location
- Chantilly, VA, USA
- conference start
- 2009-10-25
- conference end
- 2009-10-26
- Web of Science type
- Proceedings Paper
- Web of Science id
- 000279343200010
- ISSN
- 0302-9743
- ISBN
- 978-3-642-05081-7
- DOI
- 10.1007/978-3-642-05082-4_10
- language
- English
- UGent publication?
- yes
- classification
- P1
- copyright statement
*I have transferred the copyright for this publication to the publisher*- id
- 861391
- handle
- http://hdl.handle.net/1854/LU-861391
- date created
- 2010-02-15 08:46:43
- date last changed
- 2017-01-02 09:52:50

@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}, }

- 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.