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 eeective solution to this problem. We support this claim with the presentation of an algorithm called NUM, to which a top-down reenement operator can delegate the task of nding 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.