Common Knowledge Always, Forever

TL;DR

This paper introduces a polytopological dynamic logic capable of expressing common knowledge and its generalizations, analyzing its finite model properties over different topological spaces.

Contribution

It presents a new polytopological PDL that captures common knowledge and explores its finite model properties over closure and Cantor derivative spaces.

Findings

Finite model property over closure spaces

Lack of finite model property over Cantor derivative spaces

Embedding of linear temporal logic with 'past'

Abstract

There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model property over closure spaces but not over Cantor derivative spaces. The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property.