This paper introduces a hybrid approach for rule discovery in databases in
an environment with uncertainty and incompleteness. We first create an appr
opriate relationship between deductive reasoning and stochastic process, an
d extend the relationship for including abduction. Then, we define a Genera
lization Distribution Table (GDT), which is a variant of transition matrix
in stochastic process, as a hypothesis search space for generalization, and
describe that the GDT can be represented by knowledge-oriented networks. F
urthermore, we describe a discovery process based on the network representa
tion. Finally, we introduce some extension for making our approach more use
ful, and discuss some problems for real applications. We discuss inductive
methods from the viewpoint of the value of information, and describe that t
he main features of our approach are: (1) the uncertainty of a rule, includ
ing its ability to predict possible instances, can be explicitly represente
d in the strength of the rule, (2) noisy data and data change can be handle
d effectively, (3) biases can be flexibly selected and background knowledge
can be used in the discovery process for constraint and search control, an
d (4) if-then rules can be discovered in an evolutionary, parallel-distribu
ted cooperative mode. (C) 2000 Elsevier Science Inc. All rights reserved.