Do You Know What I Mean? A Syntactic Representation for Differential Bounded Awareness

TL;DR

This paper introduces a syntactic framework for modeling communication between agents with different world representations, focusing on translation operators and their logical properties.

Contribution

It defines translation operators between languages to approximate meanings and analyzes conditions for embedding agents' subjective states into a joint space.

Findings

Translation operators preserve some logical operations but not all.

Necessary and sufficient conditions for joint state space existence are derived.

The approach compares language expressiveness and associated state space properties.

Abstract

Without the assumption of complete, shared awareness, it is necessary to consider communication between agents who may entertain different representations of the world. A syntactic (language-based) approach provides powerful tools to address this problem. In this paper, we define translation operators between two languages which provide a `best approximation' for the meaning of propositions in the target language subject to its expressive power. We show that, in general, the translation operators preserve some, but not all, logical operations. We derive necessary and sufficient conditions for the existence of a joint state space and a joint language, in which the subjective state spaces of each agent, and their individual languages, may be embedded. This approach allows us to compare languages with respect to their expressiveness and thus, with respect to the properties of the associated state space.