Abstract
As agents faced with fallible information, we frequently find ourselves in situations where we are forced to base our beliefs on evidence which is in some way or another contradictory. We nevertheless want these beliefs to be rational.
This paper presents a simple probabilistic model of what it means for a belief based on a contradictory body of evidence to be rational. In this approach, we model contradictions in the evidence available to us as resulting from random noise, and we model our task as rational agents as reconstructing the most likely states of affairs given the evidence available to us.
Our main result consists in providing several equivalent descriptions of the non-reflexive and non-monotonic consequence relation which formalizes the notion that it is reasonable to accept that a proposition is true given good evidence supporting some set of propositions.