negative and fraction logics

between 'yes' and 'no' are all the fractions; and beyond is negative logic

We can put fractional estimates of likelihoods in a computer fixed-point format efficiently by appending '1' to the LSB least-significant-bit: the values then range from .000...05 to .999...95 - logic functions may consider the extrema as merely values in computation, and let that suffice the limits: each value, even the end-points, includes an equal portion of the whole interval - (unlike any format which represents zero and one exactly: which is spurious theoretically, having thus represented half-width intervals at those endpoints).

Statistically the 'or' and 'and' functions can be computed, a 'or' b = a+b-ab , and , a 'and' b = a*b , and at the limits the precision is retained: example a=.000...05 '0' , b=.999...95 '1' yields, a 'or' b = .999...9500...025 which rounds quickly to .999...95 , a 'and' b = .000...0499...975 which rounds to .000...05 . . . .

[under construction]

Grand-Admiral Petry
'Majestic Service in a Solar System'
Nuclear Emergency Management

© 1996