# Absolute Theorem

1. Feb 19, 2006

### powp

Hello

Does anybody know what the Absolute Theorem is in logic?? My text box uses it in proofs but I cannot find it anywhere else.

Thanks

P

2. Feb 19, 2006

### HallsofIvy

Staff Emeritus
This website:
that I found by googling "absolute theorem" and "logic" defines an absolute theorem as one whose true false value is alway TRUE for all values of its variables- what I would call a "tautology".

3. Feb 19, 2006

### powp

Thanks for you response.

What I have is this example that show the following

|- true ≡ A ≡ A

(1) true ≡ false ≡ false <axiom>
(2) false ≡ false ≡ A ≡ A <absolute theorem>
(3) true ≡ A ≡ A <Trans + (1, 2)>

My question is where does line 2 come from? Looks like it is coming from a combination of the formula I am trying to prove and line 1.

4. Feb 19, 2006

### honestrosewater

Are you leaving out grouping symbols? Can you replace them or give the rules for replacing them? What does

true ≡ A

mean?

5. Feb 19, 2006

### powp

no I am not leaving out grouping symbols. This is how this is in our text/course notes.

as for what true ≡ A mean. Offically I do not know. They want us to learn the rules before we learn what True and False mean.

I belive A would evalute to equal true. So so lost.

Thanks

6. Feb 19, 2006

### honestrosewater

Ouch. Do those notes happen to be available online?

Well, if equivalence is a binary operation, there must be grouping symbols or rules for grouping. I guess they leave them out since ((A ≡ B) ≡ C) -|- (A ≡ (B ≡ C)), but I imagine it might make a difference in which rules you can apply and how. Plus, they're just different formulas! Ack.

It looks like they just did this:

(1) true ≡ (false ≡ false) <axiom>
(2) (false ≡ false) ≡ (A ≡ A) <absolute theorem>
(3) true ≡ (A ≡ A) <Trans + (1, 2)>

Is that what Trans does -- allow you to substitute equivalent formulas? Can you just copy the Trans rule? Is it

A ≡ B, B ≡ C |- A ≡ C

Is Absolute Theorem a theorem or a rule? Is the line exactly the same in every example proof? What is A called? Formula, sentence, proposition? What are true and false called? The same thing, something-values?

Last edited: Feb 19, 2006
7. Feb 19, 2006

### powp

I tried to upload them but it is two large.

Think you can get the notes here.

http://www.cs.yorku.ca/~gt/papers/1090-notes-2005-I.pdf

Does order of operations matter when proving?? We can remove barkets based on the rules of which connectives have a higher priority.

I cannot find what the absolute theorom is. it is not listed at all.

Thanks for you help

8. Feb 19, 2006

### honestrosewater

Yeah, I found those and thought they might be it. I'm reading them now.
Yeah, I'm just now looking for that info so I can restore other brackets.
From the looks of things so far, I think it might be a Γ-theorem when Γ is empty. Oh, rock on:

9. Feb 19, 2006

### powp

Thanks for you help.

When I saw absolute theorem in the annotation I thought it be defined in the notes. But I searched and read and could not find it.

Thanks