Generating Numerical Literals During
Refinement

Simon Anthony and Alan M. Frisch

Department of Computer Science, University of York, York. YO1 5DD. UK.
Email:	{simona, frisch}@cs.york.ac.uk


Abstract. Despite the rapid emergence and success of Inductive Logic
Programming, problems still surround number handlingproblems 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.
References

1.	J. Jaffar and M. J. Maher. Constraint logic programming: A survey. Journal of
Logic Programming, 19-20:503583, 1994.
2.	J. Jaffar, S. Michaylov, P. Stuckey, and R. H. C. Yap. The CLP(R) language and
system. Technical Report RC 16292-72336, IBM Watson Research Centre, 1990.
3.	A. Karalic and Ivan Bratko. First order regression. To appear in the journal of
Machine Learning, 1997.
4.	S. Muggleton. Inverse entailment and Progol. New Generation Computing, 13:245
286, 1995.
5.	S. Muggleton and C. D. Page. Beyond first-order learning: Inductive logic programming 
with higher-order logic. Technical Report PRG-TR-13-94, Oxford University
Computing Laboratory, 1994.
6.	S. Muggleton and L. De Raedt. Inductive logic programming  theory and methods.
Journal of Logic Programming, 19-20:629679, 1994.
7.	M. Sebag and C. Rouveirol. Constraint inductive logic programming. In Proceedings
of the 5th International Workshop on Inductive Logic Programming, pages 181198.
Published as a technical report at the Katholieke Universiteit Leuven, 1995.
8.	A. Srinivasan and R. Camacho. Experiments in numerical reasoning with inductive
logic programming. To appear, 1997.
