Refinement-Based Planning as Satisfiability

A classical planning problem is the problem of computing a sequence of actions that transforms one state of the world into the desired. Traditional planners cast planning as a "split & prune" type search. These are called "refinement planners" since they start with a null plan and refine it by adding constraints. It has been shown recently that planning problems are far easier to solve when they are cast as model finding problems [2]. Some schemes for automated generation of the encodings of the planning problems in propositional logic have been designed [1]. However these schemes lack several of the refinements and preprocessing that traditional planners use. Since no single encoding has been shown to have the smallest size and the best performance, it is necessary to know what the space of the encodings is, to make a more flexible and efficient exploration of the encodings possible. The plan refinements can proceed either in the forward direction (from initial state) or in the backward direction (from goal) or both. The steps of a plan can either be totally ordered (state space planning) or partially ordered (plan space or least commitment planning). The direction of refinement affects the branching factor in the search space and the nature of step ordering affects the completeness of the knowledge of the world state (complete world state is known in forward state space planning and causal planning is devoid of this knowledge). One can also do pre-processing to prune irrelevant information. These three dimensions show that many more novel plan encodings [4] exist. We discuss some encodings from this space here. 1. State Space Encodings There are two categories of these encodings linear and parallel. In linear encodings, only one action occurs at a time step. In parallel encodings, multiple actions can occur at the same time step, if they do not interfere. The state space encoding in [1] is not sensitive to the direction of refinement. Our encodings are sensitive to the direction of refinement (to enforce directional control in the declarative