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. 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.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.23942 [cs.AI] |
| (or arXiv:2605.23942v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23942 arXiv-issued DOI via DataCite |
From: Carlo Cattani [view email]
[v1]
Wed, 29 Apr 2026 16:56:52 UTC (24 KB)
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