Probabilistic Unawareness

Mikaël Cozic ()
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Mikaël Cozic: LIS - Lettres, Idées, Savoirs - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12, IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques - UP1 - Université Paris 1 Panthéon-Sorbonne - DEC - Département d'Etudes Cognitives - ENS-PSL - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands-modal and probabilistic-of doxastic logic.

Keywords: C72; unawareness; epistemic logic; probabilistic logic JEL Classification: C70; D80 (search for similar items in EconPapers)
Date: 2016-12
Note: View the original document on HAL open archive server: https://hal.science/hal-01950702v1
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Citations: View citations in EconPapers (1)

Published in Games, 2016, 7 (4), pp.38. ⟨10.3390/g7040038⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01950702

DOI: 10.3390/g7040038

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