Foundational Proof Certificates in First-Order Logic

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.