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Absolute Theorem

  1. Feb 19, 2006 #1

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


  2. jcsd
  3. Feb 19, 2006 #2


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    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".
  4. Feb 19, 2006 #3
    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.
  5. Feb 19, 2006 #4


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

    true ≡ A

  6. Feb 19, 2006 #5
    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.

  7. Feb 19, 2006 #6


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    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
  8. Feb 19, 2006 #7
    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 [Broken]

    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
    Last edited by a moderator: May 2, 2017
  9. Feb 19, 2006 #8


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    Yeah, I found those and thought they might be it. :smile: 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:
    Last edited by a moderator: May 2, 2017
  10. Feb 19, 2006 #9
    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.

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