Vague Knowledge: Information without Transitivity and Partitions

Kerry Xiao

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arXiv · 2512.05833

Vague Knowledge: Information without Transitivity and Partitions

Kerry Xiao

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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.

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econ.TH cs.CL math.LO q-fin.GN

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Kerry Xiao. 2025-12-05. Vague Knowledge: Information without Transitivity and Partitions. https://arxiv.org/abs/2512.05833

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