Vague Knowledge: Information without Transitivity and Partitions
This work addresses the challenge of formalizing vague knowledge in economics, which is incremental as it builds on existing models by relaxing standard assumptions.
The paper tackles the problem of modeling vague knowledge by relaxing transitivity and partition assumptions in economic information models, showing that such knowledge remains informative and can only be expressed through vague communication, providing microfoundations for natural language and qualitative reasoning.
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.