Determinization in Structure Theories: A Unified Framework via Closure, Comparability, and Joint Admissibility

We develop a formal framework for constructing canonical interpretations from plural structure theories. A structure theory is a triple T = (Σ, A, I) consisting of a signature, axioms, and an inference policy, whose admissible interpretation family collects all globally consistent assignments of structural conclusions. We distinguish three levels of canonicalization: closure stabilization (per-seed convergence), global completion (seed-independent convergence), and determinization (a unique admissible interpretation). Non-determinism is classified into epistemic plurality (Type E) and structural plurality (Type S), with a refined Type S-strong subclass characterized by the absence of comm...

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