Modeling Awareness

We are unaware of many things, and unaware that we are unaware of them. But what is (un)awareness, and how does it relate to other epistemic notions such as belief, knowledge and uncertainty? This course will introduce students to multi-agent epistemic models of awareness and awareness dynamics that have been developed in philosophy, computer science and economics. 

We will start with the problem of logical omniscience for standard Kripke models of belief and knowledge, and introduce the Fagin-Halpern (FH) model of awareness, which addresses the problem by augmenting the standard Kripke model with a syntactic awareness function that bounds the domain in which the reasoning of agents applies. Taking the objects of awareness to be syntactical objects (i.e. formulas), instead of semantic objects such as events or propositions, has proven to be a quite flexible and theoretically useful approach. Indeed, early attempts of the alternative, event-based approach to modeling awareness faced the impossibility result due to Dekel, Lipman and Rustichini, which shows that there are no non-trivial awareness operators on standard state-spaces that satisfy certain plausible properties (DLR axioms). We will discuss two strategies that have been pursued in response to this impossibility result. The first strategy is to adopt a richer notion of events, which are comprised of fine-grained possibilities relativized to subject matters or expressive powers. The second strategy, which is more popular amongst philosophers, takes a more conservative approach by modelling events as coarse-grained sets of states (as in the standard state-space models), and invalidates the DLR axioms of awareness at certain “subjective"" states. We will present canonical models of awareness of each class, their sound and complete axiomatizations, and generalizations of these models that accommodate preferences and uncertainties with unawareness. We will also discuss how the different models formally and conceptually relate to each other as well as to the FH model. While we are unaware of many things, we also become aware of new things (objects, concepts, theories, possibilities, etc.), which in turn changes what we believe or know. How should an agent update her belief and uncertainties in light of awareness growth? 

In the second part of the course, we turn to the study of awareness dynamics, drawing on recent works in dynamic epistemic logic and Reverse Bayesianism. In particular, one ongoing controversy in the literature is whether there are two kinds of awareness growth, refinement (awareness of new concepts) and expansion (awareness of new possibilities), or just one. We will look at both formal and philosophical considerations for these two positions, with a focus on the open questions that remain from these discussions.

Pre-requisites: this course is largely self-contained. Familiarity with epistemic logic, dynamic epistemic logic and probability theory would be helpful, but is not assumed.