Formal Framework for Determinization in Structure Theories
A new arXiv preprint, ID 2608.07476, introduces a formal framework for determinization in structure theories, conceptualizing a structure theory as a combination of signature, axioms, and inference policy. The paper distinguishes three canonicalization levels: closure stabilization, global completion, and determinization. It classifies non-determinism into Type E (epistemic plurality) and Type S (structural plurality), with the Type S-strong subclass noted for lacking common upper bounds. Additionally, two mechanisms for canonicalization—operator-based completion and selector-based construction—are proposed, supported by sufficient structural conditions, while pure inference-based completion is shown to simplify to a specific case.
Key facts
- The paper is a new arXiv preprint with ID 2608.07476.
- It defines a structure theory as a triple (signature, axioms, inference policy).
- Three levels of canonicalization are distinguished: closure stabilization, global completion, and determinization.
- Non-determinism is classified into epistemic plurality (Type E) and structural plurality (Type S).
- Type S-strong subclass is characterized by absence of common upper bounds.
- Two canonicalization mechanisms are proposed: operator-based completion and selector-based construction.
- Sufficient structural conditions for these mechanisms are provided.
- Pure inference-based completion is shown to reduce to a specific case.
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