This functions transform a comparison or otherwise logical value to a numeric value for use in a pim.
1 2 3
a numeric value or
These functions are constructed purely for notation.
P is completely equivalent
as.numeric, apart from an extra control
to check whether it actually makes sense to do so.
PO is just short for
P(x < y) + 0.5*P(x == y)
either 0 or 1
# Check in pim