AI Model Theory: Grounded Continuation, Amalgamation, and Hallucination in Retrieval-Augmented Inference

We propose a model-theoretic framework for the analysis of inference in large language models and retrieval-augmented systems using the language of Jonsson theories, positive logic, and stable fragments. The paper does not claim that neural architectures literally compute first-order formulas layer by layer. Rather, it isolates a semantic abstraction under which contexts are represented by finite parameter sets, admissible continuations by positive partial types, and inference trajectories by staged realizations of such types. Under the Jonsson-theoretic hypotheses of inductiveness, joint embedding, and amalgamation, the ambient semantic environment admits a homogeneous-universal semantic model and a well-defined center. Inside stable grounded fragments we introduce grounded continuation pairs and show that retrieval refines continuation branches without increasing Morley rank in the finite-rank regime. We then prove that safe merging of finitely many retrieved packets is equivalent to amalgamability over the base context, while non-amalgamable retrieval yields semantic conflict. Hallucination is formalized as the realization of a structurally admissible branch outside the intended grounded fragment. Finally, we separate the proved core of the framework from its conjectural horizon concerning saturation, bounded context, and AGI. The resulting framework gives a logically disciplined bridge between classical model theory and contemporary AI semantics.