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Three-valued logic

  1. Jun 16, 2006 #1
    In addition to boolean T-F, they have an "undetermined" or "null" value N

    The truth table in the book for this logic goes like this:

    "OR"
    T v N = T
    F v N = N

    "AND"
    T ^ N = N
    F ^ N = F

    it does not make sence unless I assume N to be unknown in a sense of unknown whether N = T or F, i.e. N = (T v F).
    If N is considered to be a null it does not make sense at all! Is my assumption correct? or if not, could someone shed clarity on this :cry:
    Thanks.
     
  2. jcsd
  3. Jun 16, 2006 #2

    chroot

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    In this context, the word "null" is synonymous with "undefined" or "unknown", as you indicated in the first sentence of your post.

    - Warren
     
  4. Jun 16, 2006 #3

    NateTG

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    You might want to start with not. What is not N?

    Things are more complicated than that. In trinary logic, there are [itex]3^{3^2}=19683[/itex] possible binary operations, instead of [itex]2^{2^2}=16[/itex].
     
  5. Jun 17, 2006 #4

    HallsofIvy

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    A v B= True would be "one or both of A and B are true" while A v B= False would be "neither one is true". Now look at "T v N". I know A= T is true while I don't know about B= N. But one being true is enough: T v N= True.
    Look at "F v N". I know A= F is False but I don't know whether B= N is true of false. If it happens to be true then F v T= T but if it happens to be false, then F v F= F. Since I don't know, that's N:
    F v N= N.

    It's the opposite, of course, for and: A ^ B is True if and only if both A and B are true. With F ^ N, B= N doesn't matter. Since A= F is false, it doesn't matter what B is: F ^ "anything"= False so F ^ N= False.
    But with T ^ N, I don't know. T ^ T= True while T ^ F= False. If I don't know whether B is true or false, I don't know whether the compound A ^ B is true or false: T ^ N= N.
     
  6. Jun 17, 2006 #5
    Thanks. I think I got it now. I was just not sure why unknown is considered a null....
     
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