Fundamentals and Advances in Computer ScienceALGEBRAIC-DYNAMIC FORMALIZATION APPLIED TO THE MDEI MODEL: FROM THE VECTOR TABLE TO THE COGNITIVE-AFFECTIVE SYSTEMALGEBRAIC-DYNAMIC FORMALIZATION APPLIED TO THE MDEI MODEL

hematical-computational framework for the modeling of cognitive-affective states in Artificial Intelligence systems. Cognitive computing represents one of the most challenging frontiers of 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 representations. The formalism is developed on solid foundations of vector algebra, differential calculus, and dynamical systems theory, with a focus on didactic clarity and conceptual depth. A highly relevant literature review is also carried out, including studies from institutions such as MIT and Stanford and recent articles in prestigious journals, which contextualizes the MDEI in the AI scenario as a cognitive extension and discusses its contribution to 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. The MDEI offers a robust framework for adaptive and resilient AIs in the face of emotional complexity, pointing the way for applications in cognitive assistants, mental health, and education. Finally, the empirical validation of the model's parameters is critically