Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this article,  introduce fuzzy equilibrium logic as a generalization of both Pearce equilibrium logic and fuzzy ansr 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.  show that our fuzzy equilibrium logic is a proper generalization of both Pearce equilibrium logic and fuzzy ansr set programming, and  locate the computational complexity of the main reasoning tasks at the second level of the polynomial hierarchy.  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,  show that a ll-known characterization of strong equivalence in Pearce equilibrium logic generalizes to our setting, yielding a practical method to verify whether two fuzzy ansr set programs are strongly equivalent. Finally, to illustrate its application potential,  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,  show how to find abductive explanations from Łukasiewicz logic theories.
['Steven Schockaert', 'Jeroen Janssen', 'Dirk Vermeir']
I am writing a research paper on a idea Fuzzy Equilibrium Logic: Declarative Problem Solving in Continuous Domains
[{"from": "human", "value": "I am writing a research paper on a idea Fuzzy Equilibrium Logic: Declarative Problem Solving in Continuous Domains"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this article,  introduce fuzzy equilibrium logic as a generalization of both Pearce equilibrium logic and fuzzy ansr 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.  show that our fuzzy equilibrium logic is a proper generalization of both Pearce equilibrium logic and fuzzy ansr set programming, and  locate the computational complexity of the main reasoning tasks at the second level of the polynomial hierarchy.  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,  show that a ll-known characterization of strong equivalence in Pearce equilibrium logic generalizes to our setting, yielding a practical method to verify whether two fuzzy ansr set programs are strongly equivalent. Finally, to illustrate its application potential,  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,  show how to find abductive explanations from \u0141ukasiewicz logic theories."}]