{"slug": "determinization-in-structure-theories-a-unified-framework-via-closure-and-joint", "title": "Determinization in Structure Theories: A Unified Framework via Closure, Comparability, and Joint Admissibility", "summary": "A new arXiv preprint (2608.07476v1) introduces a formal framework for constructing canonical interpretations from plural structure theories, classifying non-determinism into epistemic plurality (Type E) and structural plurality (Type S) and providing conditions for determinization. The authors show that pure inference-based completion reduces to a saturated closure operator under positive, non-retractive rules, and that Type S-strong theories achieve determinization via canonical selection. The framework also applies to LLM-assisted reasoning, where hallucination is viewed as unsupported canonicalization.", "body_md": "arXiv:2608.07476v1 Announce Type: new\nAbstract: We develop a formal framework for constructing canonical interpretations from plural structure theories. A structure theory is a triple T = ({\\Sigma}, A, I) consisting of a signature, axioms, and an inference policy, whose admissible interpretation family collects all globally consistent assignments of structural conclusions.\nWe 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.\nTwo canonicalization mechanisms arise: operator-based completion and selector-based construction. We provide sufficient structural conditions under which these mechanisms exist, and show 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.\nWe further show that multi-level canonicalization forms a structurally non-commutative system via staged operators, and provide a conditional classification theorem reducing theory-intrinsic mechanisms to closure or selection. The framework also applies to LLM-assisted reasoning, where hallucination can be viewed as unsupported canonicalization.", "url": "https://wpnews.pro/news/determinization-in-structure-theories-a-unified-framework-via-closure-and-joint", "canonical_source": "https://arxiv.org/abs/2608.07476", "published_at": "2026-08-11 04:00:00+00:00", "updated_at": "2026-08-11 04:15:51.819436+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research"], "entities": ["arXiv"], "alternates": {"html": "https://wpnews.pro/news/determinization-in-structure-theories-a-unified-framework-via-closure-and-joint", "markdown": "https://wpnews.pro/news/determinization-in-structure-theories-a-unified-framework-via-closure-and-joint.md", "text": "https://wpnews.pro/news/determinization-in-structure-theories-a-unified-framework-via-closure-and-joint.txt", "jsonld": "https://wpnews.pro/news/determinization-in-structure-theories-a-unified-framework-via-closure-and-joint.jsonld"}}