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

• URL: http://arxiv.org/abs/2605.23942v1
• Date: Wed, 29 Apr 2026 16:56:52 GMT
• Title: A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence
• Abstract summary: The model is interpreted as a feedback system integrating transformation, observation, and stabilization.<n>A concrete linguistic application shows how context-dependent interpretation can be modeled as a trajectory toward a stable semantic class.
• Score: 0.17188280334580194
• License: http://creativecommons.org/licenses/by/4.0/
• 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 \[ X_{t+1} = π\big(F(f(X_t))\big), \] 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 stability. To demonstrate the operational character of the framework, a computational illustration is provided, together with a qualitative analysis of the induced dynamics. A concrete linguistic application shows how context-dependent interpretation can be modeled as a trajectory toward a stable semantic class. The proposed approach connects dynamical systems, category theory, and cognitive modeling, and provides a unified representation of cognition as a feedback-driven process evolving toward invariant interpretations.

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