  Probabilistic systems are an important theme in AI domain. As the
specification language, the logic PCTL is now the default logic for reasoning
about probabilistic properties. In this paper, we present a natural and
succinct probabilistic extension of mu-calculus, another prominent logic in the
concurrency theory. We study the relationship with PCTL. Interestingly, the
expressiveness is highly orthogonal with PCTL. The proposed logic captures some
useful properties which cannot be expressed in PCTL. We investigate the model
checking and satisfiability problem, and show that the model checking problem
is in UP and co-UP, and the satisfiability checking can be decided via reducing
into solving parity games. This is in contrast to PCTL as well, whose
satisfiability checking is still an open problem.
