I've been working with a form of multi-valued logic in which variables are
interpreted as flickering between 0 and 1 so quickly that any two samplings of
the variable are independant (even within the same equation), and thus appear
to take a value somewhere in the range of 0 to 1. The value of a given
variable is interpreted as the portion of time that the variable is true.
With this interpretation, it is easy to derive formulas for any operation
directly from truth tables. For instance, if A is true A of the time, and B
is true B of the time, then (A and B) is true A*B of the time. (A or B) is
A+B- A*B. (A == B) is 1-A-B+2*A*B. etc. You can see my web page for
details on how to derive these:
www.geocities.com/CollegePark/9315/fuzzy.htm
The beauty of this system is that all the usual rules and laws of Boolean
logic still apply, like DeMorgan's rule and stuff.
Anyway, just to work an example, consider "this statement is false".
let p = "this statement is false"
.: p = (p == 0)
.: p = 1-p-0+2*p*0
.: p = 1-p
.: 2p = 1
.: p = 0.5
So, p is true half the time. This means that "this statement is false" is
true half the time, so it's false half the time, and "this statement is
false" is false the other half of the time, and therefore is true the other
half of the time. If you managed to parse that sentence then you can see
that it agrees with the result p = 0.5.
Anyways, this system is real handy for solving logic paradoxes and it has
several other neat-o properties. While in my personal opinion, this is the
"right" fuzzy logic, I realize that strictly speaking there is no "right"
fuzzy logic, so I'd like to call it something else. When most people think
about fuzzy logic they think of the common rules which have gained
acceptance, like and = min, or = max, etc., which isn't what I'm using. So
how about "stochastic logic"? Is that name taken?
- GLYPH
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