Name
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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1145/2362355.2362361 | ACM Trans. Comput. Log. |
Keywords | Field | DocType |
continuous domains,fuzzy answer set program,fuzzy logic,equilibrium logic,fuzzy equilibrium logic,declarative problem,ukasiewicz logic theory,pearce equilibrium logic generalizes,pearce equilibrium logic,fuzzy answer set programming,strong nash equilibrium,fuzzy equilibrium logic model,answer set programming | Discrete mathematics,T-norm fuzzy logics,Computational logic,Łukasiewicz logic,Fuzzy set operations,Fuzzy logic,Multimodal logic,Theoretical computer science,Artificial intelligence,Logic programming,Fuzzy number,Mathematics | Journal |
Volume | Issue | ISSN |
13 | 4 | 1529-3785 |
Citations | PageRank | References |
8 | 0.49 | 56 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Steven Schockaert | 1 | 88 | 5.91 |
| Jeroen Janssen | 2 | 71 | 6.17 |
| Dirk Vermeir | 3 | 694 | 85.34 |