Aschieri, Federico - On Natural Deduction for Herbrand Constructive Logics I: Curry-Howard Correspondence for Dummett's Logic LC

lmcs:2048 - Logical Methods in Computer Science, September 28, 2016, Volume 12, Issue 3
On Natural Deduction for Herbrand Constructive Logics I: Curry-Howard Correspondence for Dummett's Logic LC

Authors: Aschieri, Federico

Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for first-order and second-order Dummett's logic. We add to the lambda calculus an operator which represents, from the viewpoint of programming, a mechanism for representing parallel computations and communication between them, and from the viewpoint of logic, Dummett's axiom. We prove that our typed calculus is normalizing and show that proof terms for existentially quantified formulas reduce to a list of individual terms forming an Herbrand disjunction.


Source : oai:arXiv.org:1609.03190
DOI : 10.2168/LMCS-12(3:13)2016
Volume: Volume 12, Issue 3
Published on: September 28, 2016
Submitted on: September 28, 2016
Keywords: Computer Science - Logic in Computer Science


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