Thanks for that perspective. I was not aware of the Lukasiewicz distinction.
I'll look into that.
The measures where taken to be in the range 0-1, percentages or probabilities or
anything that maps isomorphically into this range.
(Specifically, I'm looking at quantum mechanical inner products, both real
symmetrical 0-1 and complex -1 to 1)
I was confused as to why A ZAND B is taken as min(A(x),B(x)) since
the ranges defined above are the correct possibilities for "A \cap B".
For instance in the case A=.1 and B=.2 the possible range of overlap
can be expressed graphically as:
Minimum overlap
1234567890
A =
B ==
-0-
Maximum overlap
1234567890
A =
B ==
- .1
Minimum overlap
1234567890
A ======
B ========
---- .4
for A=.6 and B=.8
Maximum overlap
1234567890
A ======
B ========
------ .6
(or use overlapping pie charts)
If A = percentage of students failing question A and,
B = percentage of students failing question B,
then if
C = percentage of students failing both questions A and B,
C will lie in these ranges, and C < = A ZAND B,
what is the rational for A ZAND B = min(A(x),B(x)) then ?
--http://www.bestweb.net/~ca314159/
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