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Epistemic Foundations for Set-algebraic Representations of Knowledge

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  • Satoshi Fukuda

Abstract

This paper formalizes an informal idea that an agent's knowledge is characterized by a collection of sets such as a -algebra within the framework of a state space model of knowledge. The formalization is based on the agent's logical and introspective abilities and on the underlying structure of the state space. The agent is logical and introspective about what she knows if and only if her knowledge is summarized by a collection of events with the property that, for any event, the collection has the maximal event included in the original event. When the underlying space is a measurable space, the collection becomes a -algebra if and only if the agent is additionally introspective about what she does not know. The paper characterizes why the agent's knowledge takes (or does not take) such a set algebra as a -algebra or a topology, depending on the agent's logical and introspective abilities and on the underlying environment. Journal of Economic Literature Classification Numbers: C70, D83 Keywords: Knowledge,Information, Set Algebra, -algebra, Introspection

Suggested Citation

  • Satoshi Fukuda, 2018. "Epistemic Foundations for Set-algebraic Representations of Knowledge," Working Papers 633, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:633
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    Citations

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    Cited by:

    1. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    2. Satoshi Fukuda, 2018. "Representing Unawareness on State Spaces," Working Papers 635, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    4. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    5. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    6. Áron Tóbiás, 2021. "A unified epistemological theory of information processing," Theory and Decision, Springer, vol. 90(1), pages 63-83, February.
    7. Fukuda, Satoshi, 2020. "Formalizing common belief with no underlying assumption on individual beliefs," Games and Economic Behavior, Elsevier, vol. 121(C), pages 169-189.
    8. Áron Tóbiás, 2021. "Meet meets join: the interaction between pooled and common knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 989-1019, December.

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    More about this item

    Keywords

    knowledge; information; set algebra; -algebra; introspection;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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