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arXiv · 2312.16480

Permissive-Nominal Logic (journal version)

Gilles Dowek·Murdoch J. Gabbay
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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 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.

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Gilles Dowek, Murdoch J. Gabbay. 2023-12-27. Permissive-Nominal Logic (journal version). https://doi.org/10.1145/2287718.2287720

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