A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence

This paper proposes a structural and dynamical framework for modeling cognitive processes within a cybernetic perspective. Cognitive states are represented as elements of a state space evolving through an iterative update rule of the form \[ X_{t+1} = π\big(F(f(X_t))\big), \] where $f$ describes internal transformations, $F$ represents interpretative mappings, and $π$ enforces semantic equivalence. The model is interpreted as a feedback system integrating transformation, observation, and stabilization. A categorical formulation is introduced to capture compositional structure, while the associated dynamics are analyzed through fixed-point arguments and contraction conditions ensuring stab...

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