Planning Using Abstraction Based on Homomorphism

Abstract

In order to solve a complicated problem, we often simplify the problem into a more manageable abstract problem and obtain information for the original problem by solving it in an abstract form and by utilizing the abstract solution. Such technique is widely used in problem solving or planning. In the Conventional Planning system (ABSTRIPS), abstraction depends on the representation of rules (preconditions, deletion lists, addition lists) and only the precondition of the operator is abstracted by deleting atoms. In this paper we propose a new abstraction method based on homomorphism, where planning problems are formalized by logic programs on specialization system and are abstracted by homomorphism to abstract problems. Specialization system is the structure which consists of atoms and substitutions. Concrete problem or abstract problem is written by its own specialization system. We call a mapping from a concrete problem to a abstract problem 'homomorphism'. As compared with conventional planning systems, our method has advantages, especially regarding the following two points. The first is to be able to abstract not only the operators but also the states of the planning problems. The second is to have a homomorphism theorem, which provides the theoretica1 basis for the abstraction method in this paper.