ALGEBRAIC-DYNAMIC FORMALIZATION APPLIED TO THE MDEI MODEL: FROM THE VECTOR TABLE TO THE COGNITIVE-AFFECTIVE SYSTEM

Abstract

This article introduces an enhanced Internal State Dynamics Model (MDEI), a mathematical-computational framework for modeling cognitive-affective states in Artificial Intelligence systems. Cognitive computing represents one of the most challenging frontiers in modern AI, evolving from simplified models to sophisticated dynamic approaches inspired by brain functioning. In MDEI, each internal state is represented by an adaptive three-dimensional vector, surpassing traditional discrete symbolic approaches. The formalism is built on solid foundations of vector algebra, differential calculus, and dynamical systems theory, with an emphasis on didactic clarity and conceptual depth. A strategic literature review, including studies from MIT, Stanford, and recent high-impact journals, situates MDEI within the perspective of AI as a cognitive extension, highlighting its role in facilitating more natural human-machine interactions. Recent research demonstrates that advanced generative systems exhibit behaviors aligned with human cognitive functions, indicating potential for human-machine synergy. MDEI provides a robust framework for developing adaptive, resilient AI in the face of emotional complexity, pointing to applications in cognitive assistants, mental health, and education. Finally, the empirical validation of the model's parameters is critically discussed, underscoring the need for future experimental work based on rigorous emotional assessment methods.