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Complementary Logic

  1. Nov 6, 2003 #1
    Dear peolpe,

    I am a poor formalist, but have some ideas, which are based on structural|quantitative point of view on Math language.

    They can be found here: http://www.geocities.com/complementarytheory/CATpage.html

    Maybe you can help me to address these ideas in a rigorous formal way.

    By doing it, we can check what idea can survive rigorous definitions.

    I think that only then we can move to the next step, which is: to examine its originality.

    Thank you,

    Yours,

    Organic

    ----------------------------------------------------------------------------
    Short overview:

    Boolean logic is based on 0 Xor 1.

    Fuzzy logic is fading transition between 0 Xor 1.

    A non-Boolean logic is based on 0 And 1.


    My point of view leading me to what I call Complementary logic, which is a fading transition between Boolean logic (0 Xor 1) and non-boolean logic (0 And 1), for example:

    Number 4 is fading transition between multiplication 1*4 and addition ((((+1)+1)+1)+1) ,and vice versa.

    This fading transition can be represented as:
    Code (Text):
     
    (1*4)=              (1,1,1,1) <------------- Maximum symmetry-degree,
    ((1*2)+1*2)=        ((1,1),1,1)              Minimum information's clarity-degree (no uniqueness)
    (((+1)+1)+1*2)=     (((1),1),1,1)
    ((1*2)+(1*2))=      ((1,1),(1,1))
    (((+1)+1)+(1*2))=   (((1),1),(1,1))
    (((+1)+1)+((+1)+1))=(((1),1),((1),1))
    ((1*3)+1)=          ((1,1,1),1)
    (((1*2)+1)+1)=      (((1,1),1),1)
    ((((+1)+1)+1)+1)=   ((((1),1),1),1) <------ Minimum symmetry-degree,
                                                Maximum information's clarity-degree (uniqueness)
     
    Multiplication can be operated only among objects with structural identity .

    Also multiplication is noncommutative, for example:

    2*3 = ( (1,1),(1,1),(1,1) ) or ( ((1),1),((1),1),((1),1) )

    3*2 = ( (1,1,1),(1,1,1) ) or ( ((1,1),1),((1,1),1) ) or ( (((1),1),1),(((1),1),1) )

    Through my point of view, there are connections between structure's symmetry-degree and information's clarity-degree.

    High Entropy means maximum level of redundancy and uncertainty, which are based on the highest symmetry-degree of some system.

    For example let us say that there is a piano with 3 notes and we call it 3-system :

    DO=D , RE=R , MI=M

    The highest Entropy level of 3-system is the most left information's-tree,
    where each key has no unique value of its own, and vice versa.
    Code (Text):
     
    <-Redundancy->
        M   M   M  ^<----Uncertainty
        R   R   R  |    R   R
        D   D   D  |    D   D   M       D   R   M
        .   .   .  v    .   .   .       .   .   .
        |   |   |       |   |   |       |   |   |
    3 = |   |   |       |___|_  |       |___|   |
        |   |   |       |       |       |       |
        |___|___|_      |_______|       |_______|
        |               |               |    
     
    An example of 4-notes piano:

    DO=D , RE=R , MI=M , FA=F
    Code (Text):

    ------------>>>

        F  F  F  F           F  F           F  F
        M  M  M  M           M  M           M  M
        R  R  R  R     R  R  R  R           R  R     R  R  R  R
        D  D  D  D     D  D  D  D     D  R  D  D     D  D  D  D
        .  .  .  .     .  .  .  .     .  .  .  .     .  .  .  .
        |  |  |  |     |  |  |  |     |  |  |  |     |  |  |  |
        |  |  |  |     |__|_ |  |     |__|  |  |     |__|_ |__|_
        |  |  |  |     |     |  |     |     |  |     |     |
        |  |  |  |     |     |  |     |     |  |     |     |
        |  |  |  |     |     |  |     |     |  |     |     |
        |__|__|__|_    |_____|__|_    |_____|__|_    |_____|____
        |              |              |              |

    4 =
                                       M  M  M
              R  R                     R  R  R        R  R
        D  R  D  D      D  R  D  R     D  D  D  F     D  D  M  F
        .  .  .  .      .  .  .  .     .  .  .  .     .  .  .  .
        |  |  |  |      |  |  |  |     |  |  |  |     |  |  |  |
        |__|  |__|_     |__|  |__|     |  |  |  |     |__|_ |  |
        |     |         |     |        |  |  |  |     |     |  |
        |     |         |     |        |__|__|_ |     |_____|  |
        |     |         |     |        |        |     |        |
        |_____|____     |_____|____    |________|     |________|
        |               |              |              |


        D  R  M  F
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  |
        |_____|  |
        |        |
        |________|
        |    
     
     
    Last edited: Nov 6, 2003
  2. jcsd
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