A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence
Authors: Carlo Cattani, Dioneia Motta Monte-Serrat
Organizations: Engineering School, DEIM, University of Tuscia, (VT), 01100, Italy · Department of Physics, University of Sao Paulo, USP; Department of Law, University of Ribeirao Preto, Unaerp, Brazil.
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
Xt+1=π(F(f(Xt))),
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.
Predictive processing theories portray the brain as a hierarchical prediction engine that minimizes prediction error, yet they lack operational definitions for the structure of a "prediction," the standardized response to a prediction error, and the mechanism that maintains consistency across successive updates. Bayesian cognitive science attempts to subsume all uncertainty under probabilistic belief updating, but it presupposes a closed hypothesis space and provides no generative account of how the objects over which probabilities are distributed become discrete, identifiable referents in the first place. This paper introduces Predictive Set Theory (PST), a formal generative framework that reconstructs cognitive architecture from first principles. PST anchors cognition in a minimal set of operations---a sensor formalized as an identity function, set-theoretic state refresh, and three fundamental forms of reference chains (reference, counter-reference, and semi-reference)---and rigorously derives core cognitive functions including state sequences, demand, comparison, efficiency, and finite-horizon probabilistic planning. Rather than modeling neural mechanisms, PST constitutes a design specification for any system that must maintain internal consistency while acting under incomplete information and irreversible risk. The framework offers novel resolutions to classical problems such as Russell's paradox, the cognitive status of Gödelian incompleteness, the grounding of negative feedback, and the comprehension of film editing. The primary purpose of this paper is to establish, through the public academic record, the originality and completeness of the Predictive Set Theory framework.
We reinterpret Transformer inference by developing a functionally equivalent mechanical-structural description of its functional architecture. Parameterized transformations of token representations, or transforming concepts, are identified with simple neural networks organized through output-input and output-weight interconnections. This redescription makes explicit an organizational feature that is not equally salient in the standard matrix description: during inference, the outputs of some networks determine the weights, and hence the transformations, of others. These output-weight interconnections generate prompt-dependent dynamic transformations and give rise to Sequence-level Interactive Dynamic Parallel Processing (SIDPP). We show that the number of dynamic parameters grows linearly with prompt length and may become comparable to, or exceed, the number of static parameters fixed through training, a phenomenon we call strong prompt sensitivity. Philosophically, this shifts the conceptual picture of the Transformer from one centered on the static structure acquired through training to one that also treats the prompt-dependent transformations dynamically constructed during inference as constitutive features of its operation. GPT-4.5's recent Turing test results provide a behavioral illustration of this phenomenon. Finally, we identify biological mechanisms morphologically and functionally correspondent to output-weight interconnections, supporting the in-principle neural realizability of SIDPP and motivating Conjecture T: human neural systems may realize a functional architecture relevantly similar to that of the Transformer.
The linguistic notion of state has traditionally been restricted to the construct (annexation) state of Afroasiatic languages and treated as a language-specific morphosyntactic phenomenon. This article argues instead that the state is a systemic, context-dependent morphosyntactic mechanism that selects grammatical templates across synthetic languages. Within the Template-Based Modular Cognitive framework, taking Riffian as its primary empirical basis, the proposed theory provides a unified explanation for diverse nominal marking patterns traditionally analysed independently and is formalised as a symbolic computational model in which the state is represented by a set-valued function over grammatical templates. A learning algorithm based on finite-set operations acquires and predicts state-dependent grammatical configurations. Beyond nominal morphology, the framework has broader implications for theories of nominal structure and lexical cognition, in particular offering a unified analysis of determiner-noun structure. These results suggest that the state constitutes one instance of a broader class of syntactically conditioned dependencies that also includes agreement and grammatical case.