Generating Numerical Literals During Refinement

. Despite the rapid emergence and success of Inductive Logic Programming, problems still surround number handling---problems directly inherited from the choice of logic programs as the representation language. Our conjecture is that a generalisation of the representation language to Constraint Logic Programs provides an effective solution to this problem. We support this claim with the presentation of an algorithm called NUM, to which a top-down refinement operator can delegate the task of finding numerical literals. NUM can handle equations, in-equations and dis-equations in a uniform way, and, furthermore, provides more generality than competing approaches since numerical literals are not required to cover all the positive examples available. 1 Introduction Many of the concepts that we might wish to learn involve numbers. However, within the Inductive Logic Programming (ILP) paradigm [6], such numerical reasoning is poorly handled---a problem inherited from the choice of logic progr..