Matematické Fórum

↑ lddangsta:
A co, poctivci mají velké nosy a padouší velké uší? (chtělo by asi napsat kdo jak odpovídá na položené otázky)

↑ lddangsta:

Řešením je takzvaný Goodmanův princip. Bohužel se mi nepodařilo najít na netu český odkaz, ale zde je úrovek z Smullyanovy Satan, Cantor a nekonečno v originále:

If you ask the native whether the left road is the one that leads to the palace, the question will be useless, since you have no idea whether he is a knight or a knave. The right question to ask is “Are you the type who would claim that the left road leads to the palace?” After getting an answer, you will have no idea whether he is a liar or a truth-teller, but you will know which road to take. More specifically, if he answers yes, you should take the left road; if he answers no, you should take the right road. The proof of this is as follows.

Suppose he answers yes. If he is a knight, then he has told the truth; he is the type who would claim that the left road leads to the palace. Hence the left road is the road to take. On the other hand, if he is a knave, his answer is a lie, which means he is not the type who would claim that the left road leads to the palace; only one of the opposite type—a knight—would claim that the left road leads to the palace. But since a knight would claim that the left road leads to the palace, then again the left road really does lead to the palace. Regardless of whether the yes answer is the truth or a lie, the left road leads to the palace.

Suppose now that the native answers no. If he is truthful, then he is really not the type who would claim that the left road leads to the palace; only a knave would claim that. And since a knave would make that claim, the claim is false, which means that the left road does not lead to the palace. On the other hand if he is lying, then he really would claim that the left road leads to the palace (since he says he wouldn’t), but, being a knave, his claim would be false, which means that the left road doesn’t lead to the palace. This proves that if he answers no, the right road is the one to take, regardless of whether the native lied or told the truth.

The Goodman principle is really a remarkable thing. Using it, one can extract any information from one who either always lies or always tells the truth. Of course, this strategy won’t work on someone who sometimes tells the truth and sometimes lies.

... kde je to vysvětleno

Napadla mě velmi zajímavá otázka, jak zjistit platnost výroku V, a ani dotyčná osoba nepotřebuje znát svůj "typ":
"Co byste mi odpověděl, kdybych se vás zeptal, zda V platí?"
Vlastně tak lhář použije dvojitou negaci a tedy řekne skutečnou pravdivostní hodnotu V.