2019/07/22 by Malvin Gattinger, Yanjing Wang
Computer Science · #cs.LO
paper · pdf · doi:10.4204/eptcs.297.14
published as EPTCS 297, 2019, pp. 206-220 · In Proceedings TARK 2019, arXiv:1907.08335
arxiv created 2019/07/22 · arxiv updated 2019/07/23
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.