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Planning with abstraction based on partial predicate mappings

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Abstract

Planning with abstraction is an act of finding an abstract plan that can be instantiated into a concrete plan for a given planning problem. It is very important for an abstract planning system to satisfy a property, calledDownward-Solution Property (DSP), that any abstract plan can always be instantiated into a concrete plan. J. D. Tenenberg has proposed a framework for constructing a planning system satisfying DSP. The system is constructed by abstracting operators under a givenpredicate mapping f to obtain abstract operators. Intuitively speaking, the predicate mapping corresponds to an inheritance hierarchy of concepts with which the planning is concerned. However, the condition for abstracting operators is so strong that there exist many cases whereonly a few abstract operators are obtained. Consequently, the system often generates only a very small abstract search space, and therefore fails to find a plan for a given problem at concrete level. The aim of this paper is to provide a new revised framework according to which we can construct a more flexible abstract planning system still preserving DSP. For this purpose, we introduce a notion ofpartial predicate mapping. Partial predicate mappings are computed from concrete operators andf. Intuitively, computing them corresponds to refiningf into mappings under which it is possible to obtain more number of abstract operators. Furthermore, some experimental results show that using our abstraction based on partial predicaate mappings is useful to improve planning efficiency.

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Authors and Affiliations

  1. Department of Systems Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, 227, Yokohama, Japan

    Yoshiaki Okubo & Makoto Haraguchi

Authors
  1. Yoshiaki Okubo
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  2. Makoto Haraguchi
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Additional information

Yoshiaki Okubo: He is currently a graduate student of Doctor Course of Department of Systems Science, Tokyo Institute of Technology. He received the B. E. degree in 1990 from Chiba University and the M. E. degree in 1992 from Tokyo Institute of Technology. He has been studying on planning and SLD-refutation with abstractions. In these studies, providing appropriate abstractions is an important task to improve their efficiencies. However such a task is very difficult. His current research interest is to automatically construct appropriate abstractions in SLD-refutation depending on a goal to be proven.

Makoto Haraguchi, Dr. Sci.: He received the B. S. degree in 1976, the M. S. degree in 1978 and the Dr. Sci. degree in 1984 all in Mathematics from Kyushu University. Presently, he is an Associate Professor of Systems Science, Tokyo Institute of Technology. Analogy has been his major research theme. The study of analogy involves other types of knowledge and reasoning such as induction, deduction, abstraction and abduction. Therefore, his research interests cover deductive logic, inductive logic, non-monotonic reasoning and knowledge representation. Especially he takes notice of algebraic semantics of terminological logic to make our knowledge representation more flexible. In addition, he tries to apply these fundamental studies to the research field of legal reasoning in order to build a system for legal arguments.

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Okubo, Y., Haraguchi, M. Planning with abstraction based on partial predicate mappings. New Gener Comput 12, 409–437 (1994). https://doi.org/10.1007/BF03037355

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  • DOI: https://doi.org/10.1007/BF03037355

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