Self-referentiality in Justification Logic
Logic
2020-01-28 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1902.01106,
title = {Self-referentiality in Justification Logic},
author = {Nathan Sebastian Gass and Thomas Studer},
journal= {arXiv preprint arXiv:1902.01106},
year = {2020}
}