Epistemic Informativeness

Abstract

In this paper, we introduce and formalize the concept of epistemic informativeness (EI) of statements: the set of new propositions that an agent comes to know from the truthful announcement of the statements. We formalize EI in multi-agent Public Announcement Logic and characterize it by proving that two basic statements are the same in EI iff the logical equivalence of the two is common knowledge after a certain announcement. As a corollary applied to identity statements, a= b and a= a are different in EI iff a= b is not common knowledge. This may shed new light on the differences in cognitive value of a= a and a= b, even when they are both known to be true, as long as a= b is not commonly known to all.