# Re: stochastic logic

WSiler (wsiler@aol.com)
Sun, 27 Sep 1998 00:31:23 +0200 (MET DST)

>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.

Actually, I think this is a pretty neat demonstration. Of course, the clue to
this particular multi-valued logic is the statistical independence of you
microevents. But suppose they are not independent? If the correlation between
the microevents is as positive as possible, you will get the Zadeh max-min
logic; if it is as negative as possible, you will get A AND B = max(0, a + b -
1) and A OR B = min(A+B, 1), etc. As I have reported elsewhere, Jim Buckley and
I have a paper coming out in Fuzzy Sets and Systems which extends this line of
thought to a family of multi-valued logics which can obey the laws of Excluded

As Earl says, the fact that you note has been known for a long time, but nobody
pays any attention to it. Believe me, that is not the stuff that is known, at
least by those of us who actually construct fuzzy expert systems, that nobody
pays any attention to.

William Siler

William Siler

Odium ignorantem est odium infantem,
sed odium savantem est odium ferentem!

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