Formal Semantics for Kolmogorov-Arnold Network Representations of Operational Games

🤖 Plain-English Summary

This paper develops a formal semantic framework for Kolmogorov-Arnold Network (KAN) representations of operational games. Theoretical results establish conditions for representation adequacy, computational tractability, and semantic preservation under aggregation operations.

🔑 Key Findings

• Operational games, as generalizations of strategic and dynamic games, provide powerful tools for modeling complex multi-agent interactions, but their analysis using traditional methods is limited due to the high dimensionality of state and strategy spaces.
• Drawing upon the constructive logical systems approach and the Kolmogorov-Arnold representation theorem, we establish rigorous mathematical foundations for embedding operational game dynamics within KAN architectures.
• The framework encompasses structural, operational, and denotational semantics, facilitating theoretical analysis of convergence properties, expressiveness, and computational complexity.

🔗 Related Resources