1989 年 4 巻 4 号 p. 389-397
EBL (explanation based learning), a framework for learning based on generalization from examples, has favorable properties for knowledge refinement in knowledge based problem solving systems. In the existing EBL, learning experiences have no coherence because each learning session is separated from the others. The purpose of knowledge refinement is to make problem solving process more efficient. Thus, in order to apply EBL to knowledge refinement, it is necessary to augment its framework to consider plural examples simultaneously and introduce appropriate operationality criteria. In this paper, the framework of EBL is augmented on plural examples, and considering relations between generalizations and operationality, a learning method is proposed to generate operational generalizations incrementally. The conceptualframework of augmented EBL is based on the generate-and-test paradigm with the generalization as a generator and the operationality as a test. This is formalized on the logic program. A generalization on one explanation structure is defined by an uninstantiation and an unresolution. This process is a generalization of the Mitchell's goal regression method. A macro table is generated from a generalization of a set of explanation structures for given examples. Operationality criteria are defined by two measures of the maximization of the usage degree and the minimization of the backtracking number. These measures reflect what is a useful macro table in pure-Prolog. The usage degree increases monotonically in the generalization space, but the backtracking number increases monotonically only in the n-usage subspace, which consists of generalizations that have usage degree of n. Therefore, minimal generalizations of the n-usage subspaces are useful to find operational generalizations. A concept of least EBG is introduced as such a generalization. There exists the least EBG for any set or explanation structures. It can be obtained by computing the least EBG of two explanation structures incrementally. They are minimal generalizations of n-usage subspaces. Thus, least EBG is usefull to find operational generalizations incrementally. A learning system with an incremental least EBG generator has been implemented. Its usefulness is demonstrated in the field of indefinite integration. It can generate complicated generalizations from a few examples, for which a huge number of examples are required in the existing SBL system. The macro tables obtained by this system are more compact and effective than those or learning systems that merely collect macros step by step.
