How to convert with Fitch ~A v B to A -> B ?

• Jun 28th 2010, 02:30 PM
devouredelysium
How to convert with Fitch ~A v B to A -> B ?
How, using the Fitch format, do I transform something of the form

~A V B
to
A -> B ?

Is it possible at all?

Thanks
• Jun 28th 2010, 02:46 PM
Plato
Quote:

Originally Posted by devouredelysium
How, using the Fitch format, do I transform something of the form

~A V B
to
A -> B ?

I want to be able to use Modus Ponens, as I have something of the form
1. A
2. ~A V B
and I pretend to conclude B. That would be easy having ~A V B in the form A -> B.

What is Fitch format?
• Jun 28th 2010, 03:10 PM
devouredelysium
It's a system used in Language, proof and logic. Something like this:
Attachment 18037
• Jun 28th 2010, 03:44 PM
Plato
Quote:

Originally Posted by devouredelysium
It's a system used in Language, proof and logic. Something like this:Attachment 18037

But I must tell how idiosyncratic, course specific, and nonstandard I find it.
It seems to me that this goes with a particular textbook, maybe computer science?
I hope you find someone here who is familiar with this approach.
But again, it does seem to me to be out of the mainstream.
• Jun 29th 2010, 12:41 AM
devouredelysium
Yes, it is used in Computer Science courses. It's a shame that not everyone uses the same system, as then it is harder to find people that can help you with answers to your questions :(.

Now, back on topic!
• Jun 29th 2010, 02:20 AM
Ackbeet
Well, you definitely need to assume $\displaystyle \neg A\vee B$. And then, since you are trying to prove $\displaystyle A\to B$, I would assume $\displaystyle A$ as starting a subproof. Then, it seems to me, you should try $\displaystyle \vee$ elimination on the assumption. Remember: that you can derive anything from a contradiction is a powerful tool! Often, you get a contradiction, and you can simply jump to your conclusion immediately in the current subproof.

Reply to Plato: I don't know how widespread Fitch is; it certainly seems all the rage at Stanford. It was the method I was taught at Virginia Tech (of course, the prof I had came from Stanford, so perhaps that explains that). The Barwise and Etchemendy book Language, Proof, and Logic uses Fitch in conjunction with the natural deduction rules.

I like the natural deduction rules, because they are an incredibly well-organized way of remembering your inference rules. It compares very well with Copi's however many rules he has. Each symbol has its introduction and elimination rule, and that's really all you have to remember.

Taken together, Fitch and natural deduction rules are a very powerful, easy-to-use system, in my opinion.
• Jun 29th 2010, 04:12 AM
devouredelysium
Thanks. Now not only did I prove A -> B from ~A v B , as the opposite, ~A v B from A -> B!
• Jun 30th 2010, 03:45 AM
Ackbeet
Excellent! Have a good one.