Logic - Introduction to Natural Deduction in Predicate Logic
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- เผยแพร่เมื่อ 6 ต.ค. 2024
- Logic - Rose - MBHS - Blair - This video contains a lengthy comparison between propositional logic and predicate logic with respect to their alphabet, syntax, semantics, and proof systems. We then modify and extend the Fitch-style natural deduction proof system to handle arguments in predicate logic. I explain the rules for introducing and eliminating quantifiers and do a few example proofs. - 10/17/2020
Part of a series: A Short Course on Natural Deduction: Fitch-style proofs for Propositional and Predicate Logic: • A Short Course on Natu...
bruh, it's literally free knowledge, explained way better than at my uni. thank you.
Very nice explained and helpful. Thank you W.Rose.
Your videos are the best. Thank you Will
Thank you so so much, these videos are so helpful! :)
Awesome video
purely awesome
9:22 for anything in the world if it P´s itself then ...it´s happy? Why only happy and not wet and happy?
I was saying: let P(a, b) mean that "a LOVES b" and let Q(a) mean that "a is HAPPY". Then the sentence ∀x [ P(x,x) → Q(x) ] means "If you love yourself, then you're happy" where 'you' is taken in the generic sense.
I have a question: why in proof number #3, on the line 2 you gave x a temporary name "a" and then you did the proof by cases, countrary on the line 12 you did firstly the proof by cases and then you named x as "a". I'd like to know if there's something different or it's actually the same.
Anyway, thank you for the explanations which are always clear
Good question! There is a difference. In proving the first half of the biconditional (lines 1-10), we start with an existential statement (line 1) and we want to conclude a disjunction (line 10). Any time you start with an existential statement as a premise (or an assumption) you will use existential elimination, and the first step will be to start a new subproof, eliminate the existential quantifier, and assign a temporary name to the variable. this is the only thing you can do when starting with an existential statement (existential elimination). That is why Mr. Rose immediately gave x the temporary name 'a' on line 2. The result on line 2 is a disjunction, so Mr. Rose proceeded with disjunction elimination (proof by cases) on lines 3-9.
Proving the second half of the biconditional (lines 11-22) is a different story. Here we start with a disjunction (line 11) and we want to conclude an existential statement (line 22). Given that the initial assumption is a disjunction, disjunction elimination is the way to start - which is exactly what Mr. Rose did. Both disjuncts are themselves existential statements in this case, and as I mentioned above, the only thing you can do with existential statements is existential elimination - which involves immediately assigning a temporary name to the variable. That is why Mr. Rose gave x the temporary name 'a' after starting the proof by cases in lines (11-22).
B 0:12 0:14 0:16
this guy sold me fent