Tiago Aguioncio Vieira

This paper develops a unified dynamical framework integrating affective and semantic processes in cognition. The Internal State Dynamics Model (ISDM) formalizes emotional regulation as a continuous internal state process governed by energetic constraints and Lyapunov stability, while the Teleological Semantics Model (TSM) formalizes semantic dynamics as a structured flow within a semantic field organized by local transformations and a global teleological operator. By expressing both models as differential dynamical systems, we embed affective and semantic dynamics into a common product space and introduce coupling operators that allow bidirectional interaction without reduction. Emotional states modulate semantic transitions, while semantic structure regulates affective stability, preserving the internal logic of each subsystem. A central result is the demonstration that this coupling does not destabilize the system. Under mild boundedness conditions, a joint Lyapunov functional can be constructed whose monotonic decay establishes global exponential stability of the coupled teleo– affective dynamics. Stability thus emerges not as convergence to a static equilibrium, but as a dynamic pattern of coherence arising from the interplay between energetic regulation and teleological orientation. The framework provides a mathematically minimal yet conceptually robust account of cognitive coherence, offering a non-reductive foundation for the integrated analysis of meaning and affect in both biological and artificial cognitive systems.