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This paper shows how we can combine logical representations of actions anddecision theory in such a manner that seems natural for both. In particular weassume an axiomatization of the domain in terms of situation calculus, usingwhat is essentially Reiter's solution to the frame problem, in terms of thecompletion of the axioms defining the state change. Uncertainty is handled interms of the independent choice logic, which allows for independent choices anda logic program that gives the consequences of the choices. As part of theconsequences are a specification of the utility of (final) states. The robotadopts robot plans, similar to the GOLOG programming language. Within thislogic, we can define the expected utility of a conditional plan, based on theaxiomatization of the actions, the uncertainty and the utility. The ?planning'problem is to find the plan with the highest expected utility. This is relatedto recent structured representations for POMDPs; here we use stochasticsituation calculus rules to specify the state transition function and thereward/value function. Finally we show that with stochastic frame axioms,actions representations in probabilistic STRIPS are exponentially larger thanusing the representation proposed here.

A Framework for Decision-Theoretic Planning I: Combining the Situation Calculus, Conditional Plans, Probability and Utility