  We present a unified logical framework for representing and reasoning about
both probability quantitative and qualitative preferences in probability answer
set programming, called probability answer set optimization programs. The
proposed framework is vital to allow defining probability quantitative
preferences over the possible outcomes of qualitative preferences. We show the
application of probability answer set optimization programs to a variant of the
well-known nurse restoring problem, called the nurse restoring with probability
preferences problem. To the best of our knowledge, this development is the
first to consider a logical framework for reasoning about probability
quantitative preferences, in general, and reasoning about both probability
quantitative and qualitative preferences in particular.
