First Order Regression

Abstract

We present a new approach, called First Order Regression (FOR), to handling numerical information in Inductive Logic Programming (ILP). FOR is a combination of ILP and numerical regression. First-order logic descriptions are induced to carve out those subspaces that are amenable to numerical regression among real-valued variables. The program FORS is an implementation of this idea, where numerical regression is focused on a distinguished continuous argument of the target predicate. We show that this can be viewed as a generalisation of the usual ILP problem. Applications of FORS on several real-world data sets are described: the prediction of mutagenicity of chemicals, the modelling of liquid dynamics in a surge tank, predicting the roughness in steel grinding, finite element mesh design, and operator's skill reconstruction in electric discharge machining. A comparison of FORS' performance with previous results in these domains indicates that FORS is an effective tool for ILP applications that involve numerical data.