Unawareness of theorems

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent's knowledge, but also, can impair his reasoning about what other agents know. For example, in contrast to Li (2006), Heifetz et al. (2006a) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (1976) in defining common knowledge and characterizing it in terms of a self-evident event, but departs in showing that no-trade theorems do not hold.

Theoretical Studies in Unawareness and Discovery Process

中央大学博士(経済学)【学位授与の要件】中央大学学位規則第4条第1項 【論文審査委員主査】瀧澤　弘和(中央大学経済学部教授) 【論文審査委員副査】浅田　統一郎(中央大学経済学部教授),谷口　洋志(中央大学経済学部教授),石川　竜一郎(早稲田大学国際学術院教授)application/pdfdoctoral thesi

Syntactic foundations for unawareness of theorems

We provide a syntactic model of unawareness. By introducing multiple knowledge modalities, one for each sub-language, we specifically model agents whose only mistake in reasoning (other than their unawareness) is to underestimate the knowledge of more aware agents. We show that the model is a complete and sound axiomatization of the set-theoretic model of Galanis [2007] and compare it with other unawareness models in the literature