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In standard epistemic logic, knowing that p is the same as knowing that p istrue, but it does not say anything about understanding p or knowing itsmeaning. In this paper, we present a conservative extension of PublicAnnouncement Logic (PAL) in which agents have knowledge or belief about boththe truth values and the meanings of propositions. We give a completeaxiomatization of PAL with Boolean Definitions and discuss various examples. Anagent may understand a proposition without knowing its truth value or the otherway round. Moreover, multiple agents can agree on something without agreeing onits meaning and vice versa.

How to Agree without Understanding Each Other: Public Announcement Logic with Boolean Definitions