Simplicial Belief

TL;DR

This paper introduces polychromatic simplicial complexes to model belief in modal logic, extending existing simplicial models that previously focused mainly on knowledge, and provides a new framework for plausibility relations.

Contribution

It presents a novel approach to modeling belief using polychromatic simplicial complexes, expanding the application of simplicial models in modal logic.

Findings

Defined plausibility relations on simplicial complexes.

Introduced new notions of belief within this framework.

Extended the understanding of modal logic models.

Abstract

Recently, much work has been carried out to study simplicial interpretations of modal logic. While notions of (distributed) knowledge have been well investigated in this context, it has been open how to model belief in simplicial models. We introduce polychromatic simplicial complexes, which naturally impose a plausibility relation on states. From this, we can define various notions of belief.