  Preferences play a key role in determining what goals/constraints to satisfy
when not all constraints can be satisfied simultaneously. In this work, we
study preference-based planning in a stochastic system modeled as a Markov
decision process, subject to a possible incomplete preference over temporally
extended goals. Our contributions are three folds: First, we introduce a
preference language to specify preferences over temporally extended goals.
Second, we define a novel automata-theoretic model to represent the preorder
induced by given preference relation. The automata representation of
preferences enables us to develop a preference-based planning algorithm for
stochastic systems. Finally, we show how to synthesize opportunistic strategies
that achieves an outcome that improves upon the current satisfiable outcome,
with positive probability or with probability one, in a stochastic system. We
illustrate our solution approaches using a robot motion planning example.
