Need help to Proof ~(A->B) :- A ^ ~B
I was following William Rose proof from 1 to 33. but I am stuck on this.
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1Duplicate of https://philosophy.stackexchange.com/questions/38828/how-to-prove-p-%E2%88%A7-%C2%ACq-%E2%86%94-%C2%ACp-%E2%86%92-q – Bumble Feb 22 '22 at 05:27
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Thank you, Bumble! – Keith Lam Feb 22 '22 at 08:53
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I was too tired, and I was actually at line 10 without aware of the contradiction of line 10.
Keith Lam
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1Your answer is the correct version with the right sequence of assumptions, though it should be noted since you invoked double negation in your last step so this proof/conclusion only works in classic not intuitionistic logic... – Double Knot Feb 23 '22 at 04:32
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Thank Double Knot. Unfortunately, I only taught Fitch style. May I ask how should the proof go in intuitionistic logic? – Keith Lam Feb 23 '22 at 05:44
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Intuitionistic logic is more conservative (weaker) than common classic logic and extensively used in contemporary constructive mathematics, internal logic of topos in categorical logic, type theory, automated theorem prover, and computer science, etc, and it has nothing to do with Fitch style which is a popular style of natural deduction calculus system of many logics, including classic, intuitionistic and modal logics, there's also Gentzen tree style. In IL, you just remain at line 11... – Double Knot Feb 23 '22 at 05:51