Fuzzy equilibrium logic

Schockaert, Steven ORCID: https://orcid.org/0000-0002-9256-2881, Janssen, Jeroen and Vermeir, Dirk 2012. Fuzzy equilibrium logic. ACM Transactions on Computational Logic 13 (4) , 33. 10.1145/2362355.2362361

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Abstract

In this article, we introduce fuzzy equilibrium logic as a generalization of both Pearce equilibrium logic and fuzzy answer set programming. The resulting framework combines the capability of equilibrium logic to declaratively specify search problems, with the capability of fuzzy logics to model continuous domains. We show that our fuzzy equilibrium logic is a proper generalization of both Pearce equilibrium logic and fuzzy answer set programming, and we locate the computational complexity of the main reasoning tasks at the second level of the polynomial hierarchy. We then provide a reduction from the problem of finding fuzzy equilibrium logic models to the problem of solving a particular bilevel mixed integer program (biMIP), allowing us to implement reasoners by reusing existing work from the operations research community. To illustrate the usefulness of our framework from a theoretical perspective, we show that a well-known characterization of strong equivalence in Pearce equilibrium logic generalizes to our setting, yielding a practical method to verify whether two fuzzy answer set programs are strongly equivalent. Finally, to illustrate its application potential, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria, even when players have a continuum of strategies at their disposal. As a second application example, we show how to find abductive explanations from Łukasiewicz logic theories.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher:	ACM
ISSN:	1529-3785
Last Modified:	25 Oct 2022 08:16
URI:	https://orca.cardiff.ac.uk/id/eprint/52100

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