  Generalized Probabilistic Logic (GPL) is a temporal logic, based on the modal
mu-calculus, for specifying properties of reactive probabilistic systems. We
explore XPL, an extension to GPL allowing the semantics of nondeterminism
present in Markov decision processes (MDPs). XPL is expressive enough that a
number of independently studied problems--- such as termination of Recursive
MDPs (RMDPs), PCTL* model checking of MDPs, and reachability for Branching
MDPs--- can all be cast as model checking over XPL. Termination of multi-exit
RMDPs is undecidable; thus, model checking in XPL is undecidable in general. We
define a subclass, called separable XPL, for which model checking is decidable.
Decidable problems such as termination of 1-exit RMDPs, PCTL* model checking of
MDPs, and reachability for Branching MDPs can be reduced to model checking
separable XPL. Thus, XPL forms a uniform framework for studying problems
involving systems with non-deterministic and probabilistic behaviors, while
separable XPL provides a way to solve decidable fragments of these problems.
