 Epistemic foundations for set-algebraic representations of knowledgeJournal of Mathematical Economics, 2019, vol. 84, issue C, 73-82 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. Keywords: Knowledge; Information; Set algebra; σ-algebra; Introspection (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:84:y:2019:i:c:p:73-82 DOI: 10.1016/j.jmateco.2019.07.001 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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