Canonicity in power and modal logics of finite achronal width

TL;DR

This paper introduces a method to demonstrate that certain modal logics valid in countably generated canonical frames are also valid in uncountably generated frames, with applications to finite width and new classes of multimodal logics.

Contribution

It develops a novel technique for transferring validity from countable to uncountable canonical frames in modal logic, including new classes of logics.

Findings

Validity extends from countable to uncountable frames for these logics.

Applicable to finite width and broader classes of multimodal logics.

Provides a unified approach for canonicity in various modal systems.

Abstract

We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of `finite achronal width' that are introduced here.