Rational beliefs real agents can have -- A logical point of view

The purpose of this note is to outline a framework for uncertain reasoning which drops unrealistic assumptions about the agents' inferential capabilities. To do so, we envisage a pivotal role for the recent research programme of depth-bounded Boolean logics (D'Agostino et al., 2013). We suggest that this can be fruitfully extended to the representation of rational belief under uncertainty. By doing this we lay the foundations for a prescriptive account of rational belief, namely one that realistic agents, as opposed to idealised ones, can feasibly act upon.