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Foundational proof certificates in first-order logic

Zakaria Chihani 1 Dale Miller 1 Fabien Renaud 1
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : It is the exception that provers share and trust each others proofs. One reason for this is that different provers structure their proof evidence in remarkably different ways, including, for example, proof scripts, resolution refutations, tableaux, Herbrand expansions, natural deductions, etc. In this paper, we propose an approach to foundational proof certificates as a means of flexibly presenting proof evidence so that a relatively simple and universal proof checker can check that a certificate does, indeed, elaborate to a formal proof. While we shall limit ourselves to first-order logic in this paper, we shall not limit ourselves in many other ways. Our framework for defining and checking proof certificates will work with classical and intuitionistic logics and with proof structures as diverse as resolution refutations, matings, and natural deduction.
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Submitted on : Tuesday, November 19, 2013 - 8:28:18 PM
Last modification on : Thursday, January 7, 2021 - 3:40:14 PM
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Zakaria Chihani, Dale Miller, Fabien Renaud. Foundational proof certificates in first-order logic. CADE - 24th International Conference on Automated Deduction, Jun 2013, Lake Placid, United States. ⟨hal-00906485⟩

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