  In standard epistemic logic, knowing that p is the same as knowing that p is
true, but it does not say anything about understanding p or knowing its
meaning. In this paper, we present a conservative extension of Public
Announcement Logic (PAL) in which agents have knowledge or belief about both
the truth values and the meanings of propositions. We give a complete
axiomatization of PAL with Boolean Definitions and discuss various examples. An
agent may understand a proposition without knowing its truth value or the other
way round. Moreover, multiple agents can agree on something without agreeing on
its meaning and vice versa.
