What question did this study set out to answer?

To establish a mathematical framework connecting Large Language Models to logical type realization in Jonsson theories for understanding AI inference mechanisms.

April 7, 2026Open Access

The Model Theory of Artificial Intelligence: Jonsson Semantic Spaces and Inference as Type Realization

Key Points

To establish a mathematical framework connecting Large Language Models to logical type realization in Jonsson theories for understanding AI inference mechanisms.
Developed a foundational framework mapping autoregressive generation of LLMs to logical types.
Formalized latent semantic space as a $C9^+$-homogeneous-universal model.
Analyzed the implications of this model for inductive theories in pre-training.
Proposed framework provides clarity on internal inference processes of LLMs.
Hypothesis suggests achieving AGI is equivalent to realizing a saturated model of the theory's center.

Abstract

Despite the empirical success of Large Language Models (LLMs) in demonstrating emergent cognitive abilities, a rigorous mathematical foundation explaining their internal inference mechanisms remains elusive. In this paper, we propose a novel foundational framework that maps the autoregressive generation process of AI to the realization of logical types within the context of Jonsson theories. We formalize the latent semantic space of an LLM as an ^+-homogeneous-universal semantic model Cₓ of an underlying inductive theory T acquired during pre-training. We hypothesize that the realization of Artificial General Intelligence (AGI) is mathematically equivalent to achieving a saturated semantic model of the theory's center.

The Model Theory of Artificial Intelligence: Jonsson Semantic Spaces and Inference as Type Realization

Key Points

Abstract

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