Holy cow, I wrote a book!
It's perfectly logical, which doesn't mean that it's easy to understand.
ternary raster operation
describes how three boolean values should combine to form an output
boolean. I was going to write up a description but found that the
existing documentation pretty much covers it, so I refer you to that.
In particular, look at the table that explains where PSo and DPSoo
Now, one question that has come up is "What is the algorithm for
deriving the RPN raster operation description string
from the operation index?"
The answer is, "You stare at it and use your brain's power of
pattern-matching." There is no single "correct" expression of
an operation index as RPN. For example, "DPSoo" could have been
written as "DSPoo" or "DSoPo" or as the equivalent but pointlessly
esoteric "DPoDnPnSaao". All of these expressions have the same
boolean truth table.