2019/02/04 by Nathan Sebastian Gass, Gass, Nathan Sebastian, Thomas Studer +1
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.LO
paper · pdf · doi:10.48550/arxiv.1902.01106
openalex publication_date 2019/02/04 · arxiv created 2020/01/27 · arxiv updated 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Logic of Proofs, LP, and other justification logics can have self-referential justifications of the form t:A. Such self-referential justifications are necessary for the realization of S4 in LP. Yu discovered prehistoric cycles in a particular Gentzen system as a necessary condition for S4 theorems that can only be realized using self-referentiality. It was an open problem whether prehistoric cycles also are a sufficient condition. The main results of this paper are: First, with the standard definition of self-referential theorems, prehistoric cycles are not a sufficient condition. Second, with an expansion on that definition, prehistoric cycles become sufficient for self-referential theorems.