Ambiguous Language and Differences in Beliefs

TL;DR

This paper introduces a framework for modeling ambiguous language in multi-agent systems, showing how ambiguity affects agreement results and the assumptions about shared beliefs and interpretations.

Contribution

It develops a formal model capturing ambiguity in agents' beliefs and analyzes its implications on economic agreement theorems and belief assumptions.

Findings

Ambiguity can prevent agents from reaching agreement.

Shared interpretation assumptions influence belief models.

Ambiguity impacts classical economic agreement results.

Abstract

Standard models of multi-agent modal logic do not capture the fact that information is often 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 consider the impact of ambiguity on a seminal result in economics: Aumann's result saying that agents with a common prior cannot agree to disagree. This result is known not to hold if agents do not have a common prior; we show that it also does not hold in the presence of ambiguity. We then consider the tradeoff between assuming a common interpretation (i.e., no ambiguity) and a common prior (i.e., shared initial beliefs).