We present a formal language for specifying qualitative preferences over temporal goals and a preference-based planning method in stochastic systems. Using automata-theoretic modeling, the proposed specification allows us to express preferences over different sets of outcomes, where each outcome describes a set of temporal sequences of subgoals. We define the value of preference satisfaction given a stochastic process over possible outcomes and develop an algorithm for time-constrained probabilistic planning in labeled Markov decision processes where an agent aims to maximally satisfy its preference formula within a pre-defined finite time duration. We present experimental results using a stochastic gridworld example and discuss possible extensions of the proposed preference model.
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