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An Abstract Semantics for Atoms in Nuprl

by Stuart F. Allen
2006

Abstract
We provide a supervaluating semantics for treating Atoms abstractly in Computational Type Theory, specifically for Nuprl logics. It supports a principled explanation for desirable gaps in provability without positing novel kinds of entities, nor relying in any way upon constructivity of the logic. Beyond that, though, we justify a rule that allows inference by renaming Atom values, and explore the impact of introducing this new rule upon notational definition as used in the logics.

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