A simple sequent calculus for nominal logic

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 a rgue 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 newquantifier are much simpler than in previous attempts. We als o prove several structural and metatheoretic properties, including cut-elimination, consistenc y, and equivalence to Pitts’ axiomatization of nominal logic.