Non trivial logic

[Organic]

Complementary Logic universe ( http://www.geocities.com/complementarytheory/BFC.pdf ) is an ordered logical forms that existing between a_XOR_b and a_AND_b.

For example:

Let XOR be #

Let AND be &

Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:


Uncertainty
<-Redundancy->^
d d d d |
# # # # |
c c c c |
# # # # |
b b b b |
# # # # |
{a, a, a, a} V
. . . .
| | | |
| | | |
| | | | <--(First 4-valued logical form)
| | | |
| | | |
|&_|&_|&_|_
|
={x,x,x,x}


{a, b, c, d}
. . . .
| | | |
|#_| | |
| | | <--(Last 4-valued logical form)
|#____| |
| |
|#_______|
|
={{{{x},x},x},x}


============>>>

Uncertainty
<-Redundancy->^
d d d d | d d d d
# # # # | # # # #
c c c c | c c c c
# # # # | # # # #
b b b b | b b b b b b b b b b
# # # # | # # # # # # # # # #
{a, a, a, a} V {a, a, a, a} {a, b, a, a} {a, a, a, a}
. . . . . . . . . . . . . . . .
| | | | | | | | | | | | | | | |
| | | | |&_|_ | | |#_| | | |&_|_ |&_|_
| | | | | | | | | | | |
| | | | | | | | | | | |
| | | | | | | | | | | |
|&_|&_|&_|_ |&____|&_|_ |&____|&_|_ |&____|____
| | | |
{x,x,x,x} {x,x},x,x} {{{x},x},x,x} {{x,x},{x,x}}

c c c
# # #
b b b b b b b
# # # # # # #
{a, b, a, a} {a, b, a, b} {a, a, a, d} {a, a, c, d}
. . . . . . . . . . . . . . . .
| | | | | | | | | | | | | | | |
|#_| |&_|_ |#_| |#_| | | | | |&_|_ | |
| | | | | | | | | | |
| | | | |&_|&_|_ | |#____| |
| | | | | | | |
|&____|____ |&____|____ |#_______| |#_______|
| | | |
{{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x} {{{x,x},x},x}

{a, b, c, d}
. . . .
| | | |
|#_| | |
| | |
|#____| |
| |
|#_______|
|
{{{{x},x},x},x}



A 2-valued logic is:


b b
# #
a a
. .
| |
|&__|_
|

a b
. .
| | <--- (Standard Math logical system fundamental building-block)
|#__|
|


We can see the triviality of Standard Math logical system,
when each n has several ordered logical forms between a_AND_b and a_XOR_b?

Please look at these ordered information forms http://www.geocities.com/complementarytheory/ETtable.pdf , but instead of numbers please look at them as infinitely many unique and ordered logical forms that are "waiting" to be explored and used by us.

I hope that it is understood that the flexibility of any language (including Math language) can be seen, when we examine it from the level of the information concept.