2016/09/01 by Roman V. Yampolskiy, Yampolskiy, Roman V.
Computer Science · #Artificial Intelligence (cs.AI) #Computability, Logic, AI Algorithms #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Software Engineering (cs.SE)
paper · pdf · doi:10.48550/arxiv.1609.00331
openalex publication_date 2016/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. 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.