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

Computer Science > Artificial Intelligence [Submitted on 29 Apr 2026] A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence Carlo Cattani, Dioneia Motta Monte-Serrat 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 Focus to learn more Submission history From: Carlo Cattani [view email] [v1] Wed, 29 Apr 2026 16:56:52 UTC (24 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)