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. 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…