Epistemic sentence "Agent A knows that he doesn't know the answer, but Agent A knows that Agent B also doesn't know the answer"

Question

For that sentence, I have translated it to an epistemic sentence. Can someone see if I did it right? If not, where did I go wrong?

Thanks

$K_a\land\lnot K_a\land K_a\land K_b$

Answer 1

Knowledge operators index an agent and operate on a subject (a proposition, or fact).

$\mathcal K_c\,\varphi$ means "$c$ knows $\varphi$", and here $c$ is the agent, and the proposition $\varphi$ is the subject.

You have agents $a$ and $b$ in your indices. You are missing subjects of their knowledge, such as "the answer is whatever it is."

Let's use $\varphi$ for that. Then $\mathcal K_a\mathcal K_b\varphi$ reads "$a$ knows $b$ knows the answer is whatever it is", and so forth.

Thus, to modify your attempt:

$$\mathcal K_a\neg\mathcal K_a\varphi~\land~\mathcal K_a\neg\mathcal K_b\varphi$$