  The paper explores properties of {\L}ukasiewicz mu-calculus, a version of the
quantitative/probabilistic modal mu-calculus containing both weak and strong
conjunctions and disjunctions from {\L}ukasiewicz (fuzzy) logic. We show that
this logic encodes the well-known probabilistic temporal logic PCTL. And we
give a model-checking algorithm for computing the rational denotational value
of a formula at any state in a finite rational probabilistic nondeterministic
transition system.
