p: | |
q: | |
r: | |
s: | |
t: |
~A
for $\lnot{}A$(A & B)
for $(A\land{}B)$(A | B)
for $(A\lor{}B)$(A -> B)
for $(A\rightarrow{}B)$K{a,b,c}A
for $K_{a,b,c}A$[A]B
for $[A]B$In classical logic we start with propositional variables, our propositional variables are $p$, $q$, $r$, $s$, and $t$. Each propositional variable can either be true or false. For example we can say $p$ is false, written as $\lnot p$, and let's say $q$ is true, written just as $q$.
Alongside propositional variables, we have the classical logical connectives:
(p <-> q)
in the playground.
Epistemic Logic is designed for reasoning about the knowledge of someone (we call that someone an agent). We might imagine that an agent does not know whether they are in a situation where $p$ is true, or a situation where $p$ is not true, i.e. $\lnot p$. We express situations as worlds. We express an agent's knowledge by drawing relations (arrows) between worlds. These worlds and agent relations together are called a model.
Here's an example model for when an agent $a$ doesn't know if they are in a situation where $p$, or a situation where $\lnot p$:
When you enter a classical formula into the playground, the formula is evaluated at each world as if that world was just a classical logic by itself. Epistemic logic introduces a new logical connective which takes advantage of agents' relations between worlds:
If you add more than one agent you can reason about one agent's knowledge of another agent's knowledge e.g. $K_a K_b p$, $a$ knows that $b$ knows that $p$ is true.
Finally, for the sake of representing knowledge, in Epistemic logic it is expected that all agent's relations between worlds are equivalence relations, i.e. each agent's relation is:
Dynamic Epistemic Logic introduces announcement, a mechanism for publicly announcing facts that become the knowledge of all agents. Given a formula $A$, a public announcement removes all worlds where $A$ is not true.
Dynamic Epistemic Logic also introduces a logical connective:
This project is based on the open-source Modal Logic Playground by Ross Kirsling. The Epistemic Logic Playground was made by Elliot Evans. Special thanks to my non-classical logic instructors Richard Zach and Audrey Yap, as well as my classmates Jaxson, Parker, Koray, Alejandro, and Tina who provided feedback on this project.
More resources on Epistemic Logic and this project: