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

arXiv:2605.23942v1 Announce Type: new Abstract: 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 \[ X_{t+1} = \pi\big(F(f(X_t))\big), \] where $f$ describes internal transformations, $F$ represents interpretative mappings, and $\pi$ 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 stability. To demonstrate the operational character of the framework, a computational illustration is provided, together with a qualitative analysis of the induced dynamics.