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I'm trying to figure how to study the problem of the liar and the truth teller. Here's the logic puzzle :

There are two guards and two doors. One door leads to freedom, and the other to death. One guard always lies, the other always tells the truth. They know which they are. They know where the two doors go. You do not know which guard is which or which door is which. You may ask one yes or no question. What do you ask to determine which door leads to freedom?

I have some troubles to choose the right logic to modelize this problem. I think I should use epistemic logic with Public Announcement Logic, but I don't see who is making the public announcement ? Me asking a question to a guard or the guard responding ?

logicLover
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    This has already been asked in Puzzling.SE...... –  Jan 05 '18 at 11:15
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    @Rohan I may be mistaken but it does not seem it has been asked in Puzzling.SE. The closest topic that I found there is here but does not answer my question. What topic did you saw ? – logicLover Jan 05 '18 at 11:33
  • https://puzzling.stackexchange.com/questions/2188/two-doors-with-two-guards-one-lies-one-tells-the-truth –  Jan 05 '18 at 11:35
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    Maybe my question was unclear. I am not looking for the answer to that enigma, I'm looking for the best way to modelize it with logic tools. I think the best logic we can use here is Public Announcement Logic but I have some troubles to apply it properly for I don't know which actor is doing the "public announcement" i.e. the guards or the guy who wants to go to Heaven. – logicLover Jan 05 '18 at 11:38
  • See this question. – J.-E. Pin Jan 05 '18 at 11:48
  • @logiclover Thanks! Fixed! – J.-E. Pin Jan 05 '18 at 11:54
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    Unfortunately, that post didn't really helped either for it does not rely on modal logics to modelize the problem. – logicLover Jan 05 '18 at 12:08

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