Open AccessObject-based unawareness: Axioms
Author(s) -
Oliver Board,
AUTHOR_ID,
Kim-Sau Chung,
AUTHOR_ID
Publication year - 2021
Publication title -
journal of mechanism and institution design
Language(s) - English
Resource type - Journals
eISSN - 2399-8458
pISSN - 2399-844X
DOI - 10.22574/jmid.2021.12.001
Subject(s) - axiom , introspection , sentence , object (grammar) , computer science , completeness (order theory) , key (lock) , theoretical computer science , mathematical economics , epistemology , artificial intelligence , mathematics , philosophy , computer security , mathematical analysis , geometry
This paper provides foundations for a model of unawareness, called object-based unawareness (OBU) structures, that can be used to distinguish between what an agent is unaware of and what she simply does not know. At an informal level, this distinction plays a key role in a number of papers such as Tirole (2009) and Chung & Fortnow (2016). In this paper, we give the model-theoretic description of OBU structures by showing how they assign truth conditions to every sentence of the formal language used. We then prove a model-theoretic sound and completeness theorem, which characterizes OBU structures in terms of a system of axioms. We then verify that agents in OBU structures do not violate any of the introspection axioms that are generally considered to be necessary conditions for a plausible notion of unawareness. Applications are provided in our companion paper.