Present-Day Deductive Planning

What does deductive planning really mean? Surprisingly, this question recently came up at the International Workshop on De-ductive Approaches to Plan Generation and Plan Recognition 7]. It turned out during the discussion that there are two diierent points of view. One|apparently more widespread among the American planning community|tends to use deductive for all approaches which are based on some logical formalism even if the actual planning process is carried out in an algorithmic way. In contrast to that, the second viewpoint| apparently more common in the European sector of the eld|is much stricter. Here, deductive planning is understood as solving the planning problem by the application of theorem proving methods. Thereby, a formal semantics is provided not only for the underlying logical formalism for representing planning domains, but also for the plan generation process itself, which in most cases is actually a theorem proving procedure. Deductive planning in this sense means starting from a formal plan speciication and deriving a plan by proof of the speciication formula. The plan itself is then provably correct w.r.t. this speciication. Following the latter view on deductive planning, we will focus on the important features of planning approaches based on automated theorem proving techniques. Various logics and calculi have been used for deductive planning up to now. Since the early work of Green 13], where a situation calculus domain representation was used together with a general purpose resolution theorem prover, several extensions and modi-cations have been developed. They led to eeciency gains and increased the expressive power of the underlying logic; most prominent examples being Kowalski's version of the situational calculus 21] and Manna and Waldinger's uent theory 22], respectively. Kowalski's approach provides a representational solution of the frame problem by drastically reducing the number of required frame axioms. Plans are generated using a Horn clause resolution procedure guided by several strategies. Fluent theory was the rst approach which allowed for a domain axiomatisation using exible function symbols and with that formed the basis for the generation of recursive plans. These were produced by Manna and Waldinger's resolution-based tableau calculus which also provides induction rules. The paradigm, which underlies these approaches as well as most of the more recent ones, is that of viewing plans as programs. It entails that plans are not merely action se