This article presents a mathematical model of the Motivated Emotional Mind cognitive architecture developed for embodied intelligent systems. Such a system learns to maintain its homeostasis through a generalized form of reinforcement learning based on its internal motivations, termed motivated learning (ML). The principal contribution of this article is a rigorous formalization of the re-entrant loop integrating feedforward processing, lateral interactions, and feedback pathways, together with the representational selection mechanisms that govern adaptive system responses. The model specifies how ongoing exteroceptive and interoceptive signals, bodily-motivational context, and memory traces are bound into associative memory structures termed semblions, which compete for access to further processing and top-down reconstruction. The formalization encompasses secondary perception, representational competition, curiosity, procedural gaps, and action selection directed toward limiting allostatic violations. Within this framework, motivated learning is tailored to embodied systems whose dynamics are shaped by needs, affect, and the current regulatory state. Unlike standard reinforcement-learning models, the proposed approach incorporates need thresholds, goal generation and shifting goals, bodily state, resource constraints, and action uncertainty, thereby providing a more adequate account of response selection under regulatory pressure. Global affect functions as a central control signal, modulating the learning rate, representational valence, and the balance between exploration and exploitation. The model presented here is a step toward a more rigorous formalization of cognitive phenomena and may provide a basis for further theoretical analysis, computer simulation, and implementation in artificial-intelligence systems inspired by biological processes.

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