The fun is in discrete logic! There is a whole field of mathematics (discrete mathematics) that analyzes the logic of situations that involve binary (true/false) statements, such as the solution to this riddle.

The riddle can be summed up as the following:

Let Y represent a question asked of the knights.
Let A(x) be a boolean function representing the answer of the truth-teller.
Let B(x) be a boolean function representing the answer of the liar.

B(x)≡¬A(x)

An answer can only be determined if the knights do not contradict, otherwise it could not be determined which knight was lying, for instance when Y≡(A(Y)∧B(Y))∨(¬A(Y)∧¬B(Y))≡T.
A trivial question whose answer is logically true would result in the following form:

Y≡(A(Y)∧B(Y))∨(¬A(Y)∧¬B(Y))
A(Y)≡T
B(Y)≡F
Y≡(T∧F)∨(F∧T)≡F∨F≡F
∴Y≡F

Such a question would allow identification of which knight is lying, but would not provide information on which door is true.

Let D represent a set of m doors where there is exactly 1 correct door.

∃!n∈ℕ:D(n)≡T∧n≤m

The player ideally wants to discover which value n is correct so they can choose a door accordingly.
Let R represent the following question: "What are all the doors the other knight could say are correct?".
Let S represent all possible answers to the question "What is the correct door?" for each knight respectively.
Let P be the set representing the value n where D(n)≡T, and Q be the set representing all values n where D(n)≡F,

P⊂D
P={n}
Q⊂D
Q=D-P

Thus the following properties are true:

P∩Q=∅
P∪Q=D

Consider that the answer S would be either t∈P if a knight is telling the truth or t∈Q if a knight is lying.
Thus when answering question R:

A(R)≡B(S)≡t∈Q
B(R)≡¬A(S)≡t∈Q

Since question R asks for all possible answers, both knights would provide an answer equivalent to set Q.

∴ the correct answer is D-Q; the one door that neither knight says.

I’m a little rusty on my discrete mathematics, as I haven’t done it in 3+ years, but hopefully my answer is logically sound! Feel free to correct me.

EDIT: This original puzzle is Knights and Knaves, so to be true to the original, the “truth-telling knight” is just the knight, and the “liar knight” is a knave. I just presented it this way because there was no mention of it in this comic, so I didn’t want to be confusing.