Provability: from evidence to knowledge

Esteban Peralta and Fernando Tohmé
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Esteban Peralta: University of Michigan

No 27, Working Papers from Red Nacional de Investigadores en Economía (RedNIE)

Abstract: This note explores the relationship between evidence and knowledge, when knowledge is described by a partition of a finite state space and evidence is represented by a collection of sets of messages that varies with knowledge. Fixing a partition, an event is said to be provable if there exists evidence for it in some evidence structure. We show that an event is provable if and only if it is self-evident—i.e., known at everyone of its states. We also find that knowledge is provable only if the partition of the state space is either the coarsest or the finest one. A relaxation of the conditions for provability, requiring only that some known events are provable, allows for other partitions as well. But this is only possible if we dispense with the property of monotonicity of provability. These results o?ers a novel foundation for knowledge and common knowledge, in which they emerge from the evidence held by the agents.

Keywords: Knowledge; Evidence; Common; Knowledge; Implementation (search for similar items in EconPapers)
Pages: 12 pages
Date: 2020-10
New Economics Papers: this item is included in nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:aoz:wpaper:27

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