How to Agree without Understanding Each Other: Public Announcement Logic with Boolean Definitions
Logic in Computer Science
2019-07-23 v1
Abstract
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.
Cite
@article{arxiv.1907.09105,
title = {How to Agree without Understanding Each Other: Public Announcement Logic with Boolean Definitions},
author = {Malvin Gattinger and Yanjing Wang},
journal= {arXiv preprint arXiv:1907.09105},
year = {2019}
}
Comments
In Proceedings TARK 2019, arXiv:1907.08335