The scope of provability.

We explore the relationship between evidence and knowledge when knowledge is described by a standard partition over a finite state space, and evidence is represented by a state-dependent collection of finite sets of messages. When the collection is measurable with respect to the partition, there is evidence for an event only if the event is self-evident—i.e., known at every one of its states. Thus, an event is commonly known 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 or knows nothing. The existence of partial provability outside these two extremes hinges on the non monotonic nature of provability. [ABSTRACT FROM AUTHOR]