Answer sets in a fuzzy equilibrium logic

Schockaert, Steven ORCID: https://orcid.org/0000-0002-9256-2881, Janssen, Jeroen, Vermeir, Dirk and De Cock, Martine 2009. Answer sets in a fuzzy equilibrium logic. Lecture Notes in Computer Science (5837) , pp. 135-149. 10.1007/978-3-642-05082-4_10

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software
Additional Information:	Proceedings of the Third International Conference, RR 2009, Chantilly, VA, USA, October 25-26, 2009
Publisher:	Springer Verlag
ISBN:	9783642050817
ISSN:	0302-9743
Last Modified:	20 Oct 2022 09:24
URI:	https://orca.cardiff.ac.uk/id/eprint/31832

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