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Vague Knowledge: Information without Transitivity and Partitions

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  • Kerry Xiao

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.

Suggested Citation

  • Kerry Xiao, 2025. "Vague Knowledge: Information without Transitivity and Partitions," Papers 2512.05833, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2512.05833
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    References listed on IDEAS

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