Formal Semantics for Kolmogorov-Arnold Network Representations of Operational Games

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.

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• 1 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.
• 2 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.
• 3 The framework encompasses structural, operational, and denotational semantics, facilitating theoretical analysis of convergence properties, expressiveness, and computational complexity.

This research advances how AI systems learn, reason, and solve problems — with direct implications for automation and scientific discovery.

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