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Proving (or P (not P)) in a natural deduction system

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namin

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Apr 18, 2008, 4:37:40 AM4/18/08

I am trying to prove the tautology (or P (not P)) using only the proof
rules of the system, which are Indirect Proof, Not/And/Or/Conditional/
Bicontiditonal Eliminations/Intoductions. (See the pages above for
details.)

Is it possible to prove (or P (not P)) or is there a reason why it
cannot be proved?

Thanks. ~n

namin

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Apr 18, 2008, 5:18:41 AM4/18/08

namin

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Apr 19, 2008, 12:11:06 AM4/19/08

I figured it out. It's very similar to the tough problem in the book:

1. Show (or P (not P)) (IP 2 2 3)
2. (not (or P (not P))) Asn
3. Show (or (not P) P) (OI 4)
4. Show (not P) (NI 5 2 6)
5. P Asn
6. Show (or (not P) P) (OI 5)

On Apr 18, 5:18 am, namin <na...@mit.edu> wrote:
> I am using the natural deduction system based on Kalish and Montague
> from the book, Building Problem Solver (pp. 92 - 99).

> You can view the relevant pages here:http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...http://books.google.com/books?id=MraVKw_5g28C&printsec=frontcover&sou...

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