A Model-Theoretic Framework for Retrieval-Augmented Inference: Semantic Extraction, Grounding, and Amalgamation

Retrieval-augmented systems can combine passages that are individually plausible yet jointly inconsistent, or produce a consistent answer for which no admissible source is available. This paper develops a model-theoretic framework for separating these failures. An extraction contract maps selected operational states to many-sorted first-order structures, identifies available objects, translates operational queries, and requires a satisfaction law against an independently defined verdict. The common universal--existential theory of the extracted states is inductive. We prove a criterion identifying its model class with that of a chosen inductive theory, give a nontrivial Jonsson extraction based on finite graph memory, and embed suitably small directed state families coherently into a homogeneous-universal semantic model. For a complete task-control reduct, factual license is represented by designated sets rather than by elementary realizability. Under local total transcendence and finite Morley-rank assumptions, rank and forking control branch refinement, isolated completions, and the number of informative steps. A finite retrieval batch is logically mergeable exactly when its selected types are jointly consistent; it is groundedly mergeable exactly when their union has a designated realization. Stationarity guarantees the first condition for nonforking packets, but not the second. Type-level hallucinations then divide into witness-deficient and positively camouflaged cases. These are theorems about the extracted structures. Applying them to an operational system additionally requires reflection, witness lifting, grounding certification, and architectural reachability.