Vague Knowledge: Information without Transitivity and Partitions

TL;DR

This paper introduces the concept of vague knowledge in economic models, where information is non-transitive and lacks clear partitions, highlighting its role in natural language communication and qualitative reasoning.

Contribution

It formalizes vague knowledge with non-transitive indistinguishability, expanding the understanding of information structures beyond traditional transitive and partition-based models.

Findings

Vague knowledge can distinguish some states despite lacking partitions.

Vague communication effectively expresses knowledge with blurred boundaries.

Vague knowledge remains informative even without transitivity.

Abstract

I relax the standard assumptions of transitivity and partition structure in economic models of information to formalize vague knowledge: non-transitive indistinguishability over states. I show that vague knowledge, while failing to partition the state space, remains informative by distinguishing some states from others. Moreover, it can only be faithfully expressed through vague communication with blurred boundaries. My results provide microfoundations for the prevalence of natural language communication and qualitative reasoning in the real world, where knowledge is often vague.