Abstract: Over the past 35 years, TARK successfully brought together an interdisciplinary community from computer science, logic, philosophy, economics, game theory, linguistics, psychology etc. to extend the frontier of modelling knowledge, belief, awareness and rationality. One prime example is the development of formal models for modeling awareness (e.g., Fagin and Halpern, 1988, Heifetz, Meier, and Schipper, 2006, 2008, 2013, Halpern and Rego, 2008, 2009, 2012, etc.), which recently facilitated a growing number of applications to game theory, decision theory, contract theory, financial markets, general equilibrium, business strategy, social network formation, and politics. Yet, the applied literature is in desperate need of a tractable syntax-free semantics for modelling reasoning about awareness of unawareness. I will present an extension of unawareness structures of Heifetz, Meier, and Schipper (2006) that allows for quantification over events. This enables modelling events like “I find it possible that there might exist something that I am unaware of.”, “I know that there might exist something that Joe is aware of but I am unaware of”, “I know that there might exist something that I am unaware of but others have common awareness of it even though they do not have common awareness of all the things that I might be unaware of” etc. despite knowledge and awareness retaining standard properties.
