Reopening of the conjecture about the decidability of Quasi-Dense Modal Logics (Comments on Lyon & Ostropolski-Nalewaja's result)

TL;DR

This paper discusses the unresolved question of whether quasi-dense modal logics are decidable, highlighting a flaw in prior proof and emphasizing the need for further research.

Contribution

It critically examines Lyon & Ostropolski-Nalewaja's claimed decidability result, pointing out a major flaw and reopening the question.

Findings

Prior proof contains a major flaw

Decidability of quasi-dense modal logics remains unresolved

Upper bound in EXPSPACE is not confirmed due to proof issues

Abstract

In \cite{Lyon24} the question of the decidability of quasi-dense modal logics is answered, and an upper bound in $\EXPSPACE$ is given. Unfortunately, authors' intricate proof seems to contain a major flaw that cannot be fixed, leaving the question wide open.