Applying Inductive Program Synthesis to Induction of Number Series A Case Study with IGOR2

Induction of number series is a typical task included in intelligence tests. It measures the ability to detect regular patterns and to generalize over them, which is assumed to be crucial for general intelligence. There are some computational approaches to solve number problems. Besides special-purpose algorithms, applicability of general purpose learning algorithms to number series prediction was shown for E-generalization and artificial neural networks (ANN). We present the applicability of the analytical inductive programming system Igor2 to number series problems. An empirical comparison of Igor2 shows that Igor2 has comparable performance on the test series used to evaluate the ANN and the E-generalization approach. Based on findings of a cognitive analysis of number series problems by Holzman et al. (1982, 1983) we conducted a detailed case study, presenting Igor2 with a set of number series problems where the complexity was varied over different dimensions identified as sources of cognitive complexity by Holzman. Our results show that performance times of Igor2 correspond to the cognitive findings for most dimensions.