A logic for reasoning about ambiguity

TL;DR

This paper introduces a new logical framework to model ambiguity in multi-agent systems, capturing how different agents interpret information differently and analyzing the expressive power of such logics.

Contribution

It proposes a novel logic for reasoning about ambiguity in multi-agent systems and explores various semantics reflecting agents' beliefs about ambiguity.

Findings

The proposed logic can distinguish ambiguous from unambiguous information.

Different semantics capture varying assumptions about agents' beliefs.

The logic's expressive power surpasses traditional models that lack ambiguity modeling.

Abstract

Standard models of multi-agent modal logic do not capture the fact that information is often \emph{ambiguous}, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents' beliefs regarding whether or not there is ambiguity. We examine the expressive power of logics of ambiguity compared to logics that cannot model ambiguity, with respect to the different semantics that we propose.