Permissive-nominal logic

Abstract

Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatizations with binders, such as of the λ-binder of the lambda-calculus or the ∀-binder of first-order logic. It also allows us to finitely axiomatize arithmetic, and similarly to axiomatize “nominal” datatypes-with-binding. Just like first- and higher-order logic, equality reasoning is not necessary to α-rename. This gives PNL much of the expressive power of higher-order logic, but models and derivations of PNL are first-order in character, and the logic seems to strike a good balance between expressivity and simplicity.