Dalilni tugatuvchi (QEDga o'xshash) kvadrat modal mantiqdan "majburiy ravishda" bir xil narsani talab qila oladimi?

I've only thought of this because superficially they look the same, and seem to be making similar claims. When you prove a statement P=>Q ◻, then is it the same as writing ◻P=>Q in modal logic?

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Yo'q; bu dalilning oxirini ko'rsatishning faqatgina bir usuli. Bu Halmosga taalluqli ko'rinadi ( bu erda ).
qo'shib qo'ydi muallif Mauro ALLEGRANZA, manba

1 javoblar

As Mauro indicates the original intention of Halmos was not ◻ to mean "necessarily". But if you agree that our logic holds in all possible worlds - a necessary assumption when discussing possible worlds at all - then any mathematical(!) proof A => B holds necessarily in any possible world, hence ◻(A=>B).

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qo'shib qo'ydi