This article proposes a unified mathematical framework for Artificial General Intelligence (AGI) by defining agents within a joint ((C, U, V)) space. Each AGI agent is represented by three fundamental components:
① a cognitive architecture (C), representing the internal modules, communication protocols, and theory-of-mind mechanisms;
② a set of potential functions (U), representing perceptual, cognitive, and planning capabilities (e.g., visual recognition, motion planning);
③ a set of value functions (V), describing the agent’s intrinsic drives, preferences, and social or cooperative values.
Intelligence, in this setting, emerges from the dynamic interactions between agents and their environments (physical intelligence) and among agents (social intelligence).
The paper introduces the Tong Test, a benchmark defining when an agent attains human-level intelligence ((C_h, U_h, V_h)), termed a Tong Agent. The convergence of this process defines the boundary of AGI development, conceptualized as the “stopping problem” of Tong Agents, analogous to the halting problem in Turing machines.