An Abstract Semantics for Atoms in Nuprl

http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cis/TR2006-2032
unofficial copies [PDF], [PS]


by Stuart F. Allen


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.