The scope of provability

Abstract

We explore the relationship between evidence and knowledge when knowledge isdescribed by a standard partition over a finite state space, and evidence is representedby a state-dependent collection of finite sets of messages. When the collection ismeasurable with respect to the partition, there is evidence for an event only if theevent is self-evident—i.e., known at every one of its states. Thus, an event is commonlyknown in and only if there is mutual evidence that implies that the event has occurred,and all knowledge can be proved only when the agent is informed about the state orknows nothing. The existence of partial provability outside these two extremes hingeson the non monotonic nature of provability.