A Simpler Proof Theory for Nominal Logic

Abstract. Nominal logic is a variant of first-order logic equipped with a “freshname quantifier” N and other features useful for reasoning about languages with bound names. Its original presentation was as a Hilbert axiomatic theory, but several attempts have been made to provide more convenient Gentzen-style sequent or natural deduction calculi for nominal logic. Unfortunately, the rules for N in these calculi involve complicated side-conditions, so using and proving properties of these calculi is difficult. This paper presents an improved sequent calculus NL⇒ for nominal logic. Basic results such as cut-elimination and conservativity with respect to nominal logic are proved. Also, NL⇒ is used to solve an open problem, namely relating nominal logic’s N-quantifier and the self-dual quantifier of Miller and Tiu’s FOλ .

• Type: Conference
• Year: 2005
• Where: FOSSACS
• Authors: James Cheney
• Keywords: Applied Computing, FOSSACS 2005, Natural Deduction Calculi, Nominal Logic, first-order Logic