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

@inproceedings{Gattinger2019HowTA,
  title={How to Agree without Understanding Each Other: Public Announcement Logic with Boolean Definitions},
  author={Malvin Gattinger and Yanjing Wang},
  booktitle={TARK},
  year={2019}
}
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… 
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