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Bit of a stab in the dark...

Syllogistic logic; because the premise of logic in your question shares a term with the conclusion but does not neglect a common term present in the conclusion. While the other proposition: "unlogical," is vice versa?

Edited by Somnolency
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Would it be the logic that tries to prove logic? Wouldn't that be self-referential and thus inadmissable as logic?

your all on the right track. but i will give you a clue.

i will accept is only two words but all of your answers so far are close. just refine them

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