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The reason why the brackets rule does not work is because of notational peculiarities. Associativity is not about brackets, associativity is about successive applications of an operator, which is different. And the successive applications of the implies operator yield same result independent of the
222:"This demonstrates the fact that p ⇒ q {\displaystyle p\Rightarrow q} p\Rightarrow q is logically equivalent to ¬ p ∨ q {\displaystyle \lnot p\lor q} {\displaystyle \lnot p\lor q}." Then, logically, isn't one of these functions redundant and therefore completely unnecessary?
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If you mean De Morgan duality, yes, that is right. You get the De Morgan dual by negating each operand and also the operator: for a constant that is just negating the constant. Glancing over the article didn't reveal what part in particular you are interested in. —
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investigation of truth tables in both classical and nonclassical logics, based on a strict "left-right reading" that does not require each formula to have a truth value in the set {T,F}. See also
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I'd like to have some text in the article about truth tables outside of classical logics. My first attempt ("they mostly can't be used there") was reverted by
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with a link to Sylvan.1992 which turned out to be based on
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Implies *is* associative. 𝑝→(𝑞→𝑟) should not be read as "p implies that q implies p, but "p implies q which implies r"
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However, I'm not sure I understood the papers correctly, so I'd like to have some advice from a proof theory expert.
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Better naming would be ‘number of truth tables’ (for given n; the size of a truth table for n bits is 2^n)
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459:' in the Adj row for 'Truth table for all binary logical operators' ? Adjoint is a dab listing. --
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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It appears Verum ⊤ ought to be the dual of Falsum ⊥ —OK? --
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https://en.wikipedia.org/Light%27s_associativity_test
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