Formal framework proposes determinization mechanisms for plural structure theories

A new paper on arXiv proposes a formal framework for constructing canonical interpretations from plural structure theories. The framework defines a structure theory as a triple consisting of a signature, axioms, and an inference policy, with an admissible interpretation family that collects globally consistent assignments of structural conclusions.

The authors 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 common upper bounds.

Two canonicalization mechanisms are introduced: operator-based completion and selector-based construction. The paper provides sufficient structural conditions under which these mechanisms exist and shows that pure inference-based completion reduces to a saturated closure operator under positive, non-retractive rules with an additional soundness condition.

For Type E theories, closure stabilization is established, while full determinization depends on a global confluence property that remains open. For Type S-strong theories, determinization is achieved via canonical selection. The framework also applies to LLM-assisted reasoning, where hallucination is framed as unsupported canonicalization.