Lorax, the logician
Posted Apr 8, 2023, 6:08 PM UTC
29715
Amogus 😳
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plsase no I dont even know what the weird = with tilde on it os or what a smooth n has to so with sets, I can't handle this AH spontaneously combusts
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Wtf are these logic fractions
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What the actual fuck is this
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Please Lorax help me read this.
If I’m not entirely wrong, this is a fitch proof. You have premises and proof things with those. Here you got A and B on the left and A and C on the write. Since both are true, you can conclude that (A \and B) and (A \and C) are true. Then from those you can conclude that ((A \and B) \and (A \and C)) are true. Since B is still valid as a premise, you can conclude that B -> ((…)) is true and same in the last step.
Sorry if this was meant ironically and you actually probably know this.
That ain’t fitch. No idea what it is.
I'm a CS major and this is the notation we use in your logic class. It's the same of the book Logic and Structure, by van Dallen.
I've seen some similar stuff online that uses the same natural deduction rules but builds the tree in a different format (I think that one is the Fitch one).
Well, it’s at least not the „ladder“ form as you would usually write it. But this is the way we derived the primitive formulas for the operators in our logic class.
Why are there lines above A and B? Doesn’t that denote NOT? Where does the implication come from? Never seen this form.
It's not fitch notation, but proof tree notation for natural deduction. So its using the same calculus that you're familiar with, just written in a different way.
Oh ok yeah, that makes sense. I thought this would be called fitch as well. Thanks for clearing that up!
This is just a deductive proof of a logical formula. You can read this proof bottom up. The first two steps introduce A and B as premises of the implications. Normally you would write a context on each step which is a set of formulas that are true in this step. After the implication introduction A and B are in the context (marked by 1 and 2 here). Then you prove (A and B) and (A and C) which you do by constructing two seperate proofs for each (A and B) and (A and C). (A and B) is then also split in two leafs. Both of them can be proven because the variables A and B are in the context. (The numbers 1 and 2 denote which premise from the context is used to close that leaf) The right path where (A and C) has to be proven fails because C cannot be proven (it is not in the context). The fact that the C leaf is not closed corresponds to the whole formular being not satisfied. Now go study more kekw.