### Answer Sets in a Fuzzy Equilibrium Logic

Steven Schockaert UGent, Jeroen Janssen UGent and Martine De Cock UGent (2009) 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.
author
organization
year
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
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
2010-07-28 10:25:34
```@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.