Document Type

Article

Publication Date

7-28-2017

Department

Computer Engineering and Computer Science

Abstract

Despite significant developments in proof theory, surprisingly little attention has been devoted to the concept of proof verifiers. In particular, the mathematical community may be interested in studying different types of proof verifiers (people, programs, oracles, communities, superintelligences) as mathematical objects. Such an effort could reveal their properties, their powers and limitations (particularly in human mathematicians), minimum and maximum complexity, as well as self-verification and self-reference issues. We propose an initial classification system for verifiers and provide some rudimentary analysis of solved and open problems in this important domain. Our main contribution is a formal introduction of the notion of unverifiability, for which the paper could serve as a general citation in domains of theorem proving, as well as software and AI verification.

Original Publication Information

Roman V Yampolskiy 2017 Phys. Scr. 92 093001

DOI

10.1088/1402-4896/aa7ca8

ORCID

0000-0001-9637-1161

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