A Simpler Proof Theory for Nominal Logic

Nominal logic is a variant of first-order logic which 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 paper we develop a new sequent calculus for nominal logic in which the rules for the newquantifier are much simpler than in previous attempts. We also prove several structural and metatheoretic properties, including cut-elimination, consistency, and conservativity with respect to Pitts’ axiomatization of nominal logic; these proofs are considerably simpler for our system.