NonBinary Logic (NBL)
Binary logic consists of the values True (T) and False (F) and the operators NOT(~), OR, and AND.
NOT(~)
~T=F
~F=T
F OR F = F
F OR T = T
T OR F = T
T OR T = T
F AND F = F
F AND T = F
T AND F = F
T AND T = T
etc.
Consider, however, a NonBinary Logic (NBL) consisting of the base values Neutral (N), True (T), False (F) and the operators MINUS (-), ADDITION (+), MULTIPLICATION (*), and DIVISION(/).
-N = N
-T = F
-F = T
N + N = N
N + T = T
T + N = T
N + F = F
F + N = F
T + F = N
F + T = N
T + T = 2T
F + F = 2F
etc.
N * N = N
N * T = N
T * N = N
N * F = N
F * N = N
T * F = F
F * T = F
T * T = T
F * F = T
2T * T = 2T
2F * T = 2F
etc.
For a / b, b <> N (<> means not equal to)
N / T = N
N / F = N
T / T = T
F / T = F
T / F = F
F/ F = T
2T / T = 2T
T / 2T = 1 / 2 T
2F / T = 2F
T / 2F = 1 / 2 F
etc.
Nonbinary logic forms a field (NBL, N, T, +, *) which is isomorphic to the R field (R, 0,1, +, *).
1. Associative for +
(aT + bT ) + cT = aT + (bT + cT)
2. Identity for +
aT + N = aT
3. Inverse element for +
aT + (-aT) = N
4. Commutative for +
a T+ bT = bT + aT
5. Associative for *
(aT * bT) * cT = aT * (bT * cT)
6. Identity for *
aT * T = aT
7. Inverse element for * (aT <> N ; aT not equal to N)
aT * (T/aT) = T
8. Commutative for *
aT * bT = bT * aT
9. Distributive property of * with respect +
aT * (bT + cT) = (aT * bT) + (aT * cT)
10. Isomorphism of NBL, R
NBL and R are isomorphic, with the existence of a 1 to 1 map:
NBL --> R: f(cT) = c
