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

## TL;DR

This paper extends Public Announcement Logic to include agents' knowledge about both truth and meaning of propositions, allowing for nuanced understanding of agreement and understanding in multi-agent systems.

## Contribution

It introduces a conservative extension of PAL with Boolean Definitions, providing a complete axiomatization and exploring complex knowledge scenarios.

## Key findings

- Agents can understand without knowing truth values.
- Multiple agents can agree on facts without sharing meanings.
- The logic captures nuanced epistemic states.

## 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.