Standard G\"odel modal logics are not realized by G\"odel justification logics

TL;DR

This paper demonstrates that the standard G"odel modal logics cannot be captured by G"odel justification logics, despite their relatedness through the forgetful projection, highlighting a disconnect in their realizability.

Contribution

It establishes that standard G"odel modal logics are not realizable by G"odel justification logics, clarifying the limitations of their correspondence.

Findings

G"odel modal logics are not realized by G"odel justification logics

The relationship via forgetful projection does not imply realizability

Highlights limitations in the correspondence between modal and justification logics

Abstract

We show that the standard G\"odel modal logics, as initially introduced by Caicedo and Rodriguez in \cite{CR2009,CR2010}, are not realized by the basic G\"odel justification logics although being related by the forgetful projection.