A simple sequent calculus for nominal logic

James Cheney

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arXiv · 1312.4840

A simple sequent calculus for nominal logic

James Cheney

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Abstract

Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any values considered so far). Previous attempts have been made to develop convenient rules for reasoning with the new-quantifier, but we argue that none of these attempts is completely satisfactory. In this article we develop a new sequent calculus for nominal logic in which the rules for the new- quantifier are much simpler than in previous attempts. We also prove several structural and metatheoretic properties, including cut-elimination, consistency, and equivalence to Pitts' axiomatization of nominal logic.

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James Cheney. 2013-12-17. A simple sequent calculus for nominal logic. https://arxiv.org/abs/1312.4840

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