Logical Aspects of Several Bottom-Up Fittings Author: Akihiro YAMAMOTO Source: Lecture Notes in Artificial Intelligence Vol. 1501, 1998, 158 - 168. Abstract. This research is aimed at giving a bridge between the two research areas, Inductive Logic Programming and Computational Learning. We focus our attention on four fittings (learning methods) invented in the two areas: Saturant Generalization, V*-operation with Generalization, Bottom Generalization, and Inverse Entailment. Firstly we show that each of them can be represented as an instance of a common schema. Secondly we compare the four fittings. By modifying Jung's result, we show that all definite hypotheses derived by V*-operation with Generalization can be derived by Bottom Generalization and vice versa, but that some hypotheses cannot be derived by Saturant Generalization. We also give a hypotheses of a general clause which can be derived Bottom Generalization but not by V*-operation with Generalization. We show Inverse Entailment is more powerful than other three fittings both in definite and in general clausal logic. In our papers presented at the IJCAI'97 workshops and the 7th ILP workshop, Bottom Generalization was called ``Inverse Entailment,'' but after the workshops we found it differs from Muggleton's original Inverse Entailment. We renamed it ``Bottom Generalization'' in order to reduce confusion and allow fair comparison of the fitting to others. ©Copyright 1998 Springer