Theoretical Foundations for Semantic Cognition in Artificial Intelligence

TL;DR

This work constructs a principled theory of belief for artificial agents by modeling belief as a navigable semantic manifold $\Phi$, populated with linguistically grounded ensembles and organized via abstraction levels and functional sectors. Central to the framework are the Null Tower and epistemic vacuum $\Omega$, which together explain the emergence of structured cognition through recursive abstraction and provide directional axes for epistemic orientation. The theory integrates grounding mechanisms (sensorimotor, linguistic, embodied simulation, social), dynamic belief evolution operators (Assimilation $A$, Nullification $N_t$, Annihilation $K$, Abstraction $\Lambda$, Elaboration $V$) and memory processes (Query $Q$, Retrieval $R$, Memory Assimilation $A_{mem}$), all while accounting for regulation, meta-cognition, and identity stability through concepts like Semantic Orientation and Semantic Gauge. A key contribution is the parameterized semantic architectures $\Phi^{[\theta]}$, enabling diverse agent designs (interface, reflective, tool-augmented) to share a common theoretical substrate. The framework also foregrounds embodied action via semantic execution, activation basins, and gating through reflective control, offering a cohesive path toward interpretable, self-regulating AI capable of grounding meaning, planning, and learning within a geometric cognitive space. Overall, this work offers a comprehensive, geometry-driven substrate for thinking about thinking, enabling robust grounding, memory retrieval, and regulation in future AI systems. It emphasizes cognitive plausibility, modular grounding, and the potential for cross-domain interoperability through semantic gauge and axis-based regulation.

Abstract

This monograph presents a modular cognitive architecture for artificial intelligence grounded in the formal modeling of belief as structured semantic state. Belief states are defined as dynamic ensembles of linguistic expressions embedded within a navigable manifold, where operators enable assimilation, abstraction, nullification, memory, and introspection. Drawing from philosophy, cognitive science, and neuroscience, we develop a layered framework that enables self-regulating epistemic agents capable of reflective, goal-directed thought. At the core of this framework is the epistemic vacuum: a class of semantically inert cognitive states that serves as the conceptual origin of belief space. From this foundation, the Null Tower arises as a generative structure recursively built through internal representational capacities. The theoretical constructs are designed to be implementable in both symbolic and neural systems, including large language models, hybrid agents, and adaptive memory architectures. This work offers a foundational substrate for constructing agents that reason, remember, and regulate their beliefs in structured, interpretable ways.

Figures (76)

• Figure 1: Structure of a belief state $\phi = \{ \varphi_1, \varphi_2, \ldots \}$, depicted as a network of linguistic expressions linked by semantic relations such as elaboration, generalization, support, or contradiction. This internal structure governs the coherence and dynamics of the state.
• Figure 2: Illustration of the semantic state space $\Phi$, populated by individual belief states $\phi_i$. Curved arrows depict semantic transitions among belief states.
• Figure 3: The epistemic vacuum $\Omega$ as a distinguished null region within the semantic state space $\Phi$.
• Figure 4: Semantic geometry of the belief space $\Phi$, structured by functional sectors $\Sigma$ (horizontal) and abstraction levels $k$ (vertical). Belief state $\phi$ is located at a specific $(\Sigma, k)$ cell. Vertical motion corresponds to abstraction ($\Lambda$), horizontal motion to sectoral shifts, and diagonal motion to compound transformations.
• Figure 5: The Null Tower ($\mathcal{T}_\Omega$) structure in the epistemic vacuum ($\Omega$) within semantic state space ($\Phi$).