We present a new approach, called First Order Regression (FOR), to han
dling numerical information in Inductive Logic Programming (ILP). FOR
is a combination of ILP and numerical regression. First-order logic de
scriptions 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 focus
ed on a distinguished continuous argument of the target predicate. We
show that this can be viewed as a generalisation of the usual ILP prob
lem. Applications of FORS On several real-world data sets are describe
d: the prediction of mutagenicity of chemicals, the modelling of liqui
d dynamics in a surge tank, predicting the roughness in steel grinding
, finite element mesh design, and operator's skill reconstruction in e
lectric discharge machining. A comparison of FORS' performance with pr
evious results in these domains indicates that FORS is an effective to
ol for ILP applications that involve numerical data.