Announcement as effort on topological spaces

TL;DR

This paper introduces a multi-agent logic for knowledge and announcements interpreted on topological spaces, providing axiomatizations and demonstrating completeness, with a focus on the effort modality in subset space semantics.

Contribution

It presents a new multi-agent logic with an effort modality on topological spaces, including axiomatizations and completeness proofs, advancing the theoretical understanding of announcement logic.

Findings

A new multi-agent logic of knowledge and announcements is formulated.

Axiomatizations for three variants of the logic are provided.

Completeness of these logics is established.

Abstract

We propose a multi-agent logic of knowledge, public and arbitrary announcements, that is interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, and demonstrate their completeness.