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Epistemic foundations for set-algebraic representations of knowledge

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  • Fukuda, Satoshi

Abstract

This paper formalizes an informal idea that an agent’s knowledge is characterized by a collection of sets such as a σ-algebra within the framework of a state space model. The paper fully characterizes why the agent’s knowledge takes (or does not take) such a set algebra as a σ-algebra or a topology, depending on logical and introspective properties of knowledge and on the underlying structure of the state space. The agent’s knowledge is summarized by a collection of events if and only if she can only know what is true, she knows any logical implication of what she knows, and she is introspective about what she knows. In this case, for any event, the collection that represents knowledge has the maximal event included in the original event. When the underlying space is a measurable space, the collection becomes a σ-algebra if and only if the agent is additionally introspective about what she does not know.

Suggested Citation

  • Fukuda, Satoshi, 2019. "Epistemic foundations for set-algebraic representations of knowledge," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 73-82.
    • Handle: RePEc:eee:mateco:v:84:y:2019:i:c:p:73-82
    DOI: 10.1016/j.jmateco.2019.07.001
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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, 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.
    3. Áron Tóbiás, 2021. "A unified epistemological theory of information processing," Theory and Decision, Springer, vol. 90(1), pages 63-83, February.
    4. Fukuda, Satoshi, 2020. "Formalizing common belief with no underlying assumption on individual beliefs," Games and Economic Behavior, Elsevier, vol. 121(C), pages 169-189.
    5. Satoshi Fukuda, 2018. "Representing Unawareness on State Spaces," Working Papers 635, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    7. 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.
    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; σ-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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