Re: Formal Predicate Logic

A quick question: are you allowed to use the deduction theorem?

Re: Formal Predicate Logic

I should have looked at the example. If you can use the deduction theorem and generalization, it's pretty easy. Let me post a derivation in natural deduction. It is straightforward to convert it to a derivation in .

https://lh6.googleusercontent.com/-z...800/deriv2.png

Re: Formal Predicate Logic

Hello, demode!

Re: Formal Predicate Logic

Re: Formal Predicate Logic

Well, as my derivation shows, . Then you use generalization on x. Note that x does not occur free in the assumptions, so you can apply the deduction theorem.

Re: Formal Predicate Logic

Quote:

Originally Posted by

**emakarov** Well, as my derivation shows,

. Then you use generalization on x. Note that x does not occur free in the assumptions, so you can apply the deduction theorem.

I really appreciate your response. But I'm having some trouble following your derivation in post #3, could you please show it in the simple format (like the one in my post)?

Re: Formal Predicate Logic

1. Hyp

2. K4

3. 1, 2, MP

4. instance of tautology

5. A 3, 4, MP

6. Hyp

7. K4

8. 6, 7, MP

9. 5, 8, MP

10. 9, generalization applied to x

11. 6, 10, deduction theorem

12. 1, 11, deduction theorem

In step 10, similar to part (c) of the example, generalization is a rule that must have been derived using K5. It applies to x, which is not free in either of the assumptions, so one can use the deduction theorem in steps 11 and 12.

Re: Formal Predicate Logic

I'm also stuck on a very similar question where I'm required to deduce that . And I have already shown that and . [And I want to use an instance of the tautology ]. So we have

1. Hyp

2. Hyp

3. Hyp

4. K4

5. Taut

Any ideas how to proceed? I even tried K5, but to no avail... I don't see a way to get the part inside the bracket with next to A in ~(A -> B)...

Re: Formal Predicate Logic

Since is an instance of the tautology and you have shown and , then what's the problem? Just use MP twice. Or do you need to derive ?

Re: Formal Predicate Logic

Quote:

Originally Posted by

**emakarov** Since

is an instance of the tautology and you have shown

and

, then what's the problem? Just use MP twice. Or do you need to derive

?

Edit: I get it. Thank You!