  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
axiomatisations with binders, such as of the lambda-binder of the
lambda-calculus or the forall-binder of first-order logic. It also allows us to
finitely axiomatise arithmetic, and similarly to axiomatise 'nominal'
datatypes-with-binding. Just like first- and higher-order logic, equality
reasoning is not necessary to alpha-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.
