Generative Grammars of Feasible Interaction: Theory, Dynamics, and Executable Semantics

A formal and computationally executable semantics for generative grammars of feasible interaction is presented. The framework, termed Generative Interactional Grammar (GIG), unifies structure, computation, and governance through four interlocking components: (i) GIG itself, defining admissible actions and compositions via dual semantics—category-theoretic compositionality (free monoidal presentation) and information-theoretic feasibility; (ii) the Relational Kernel Algebra (RKA), a decidable, executable fragment with confluent rewrite rules and unique normal forms; (iii) the Grammar of Relational Dynamics (GRD), which elevates grammar transformations to first-class objects and establishes fixed-point (institutionalization) results; and (iv) the Generative Kernel Engine (GKE), a neuro-symbolic induction mechanism integrating closure-aware scoring. We prove termination and confluence of RKA, ensuring deterministic reduction, and construct a compact continuous embedding linking operational dynamics to categorical semantics. The framework supports dynamic, self-governing systems in which feasible relations, rather than isolated behaviors, are the primary objects of reasoning and control. Applied across institutional analysis, protocol engineering, and multi-agent AI, GIG extends naturally to governance via meta-grammar constructs for controlled institutional change and closure-preserving verification. All core results are mechanized in Coq with reproducibility artifacts, establishing RKA as a verified computational substrate for adaptive, self-consistent systems.