Approximation of action theories and its application to conformant planning Original Research Article

This paper describes our methodology for building conformant planners, which is based on recent advances in the theory of action and change and answer set programming. The development of a planner for a given dynamic domain starts with encoding the knowledge about fluents and actions of the domain as an action theory image of some action language. Our choice in this paper is image – an action language with dynamic and static causal laws and executability conditions. An action theory image of image defines a transition diagram image containing all the possible trajectories of the domain. A transition image belongs to image iff the execution of the action a in the state s may move the domain to the state image. The second step in the planner development consists in finding a deterministic transition diagram image such that nodes of image are partial states of image, its arcs are labeled by actions, and a path in image from an initial partial state image to a partial state satisfying the goal image corresponds to a conformant plan for image and image in image. The transition diagram image is called an ‘approximation’ of image. We claim that a concise description of an approximation of image can often be given by a logic program image under the answer sets semantics. Moreover, complex initial situations and constraints on plans can be also expressed by logic programming rules and included in image. If this is possible then the problem of finding a parallel or sequential conformant plan can be reduced to computing answer sets of image. This can be done by general purpose answer set solvers. If plans are sequential and long then this method can be too time consuming. In this case, image is used as a specification for a procedural graph searching conformant planning algorithm. The paper illustrates this methodology by building several conformant planners which work for domains with complex relationship between the fluents. The efficiency of the planners is experimentally evaluated on a number of new and old benchmarks. In addition we show that for a subclass of action theories of image our planners are complete, i.e., if in image we cannot get from image to a state satisfying the goal image then there is no conformant plan for image and image in image.