Specialization of Recursive Predicates
Proceedings of the European Conference on Machine Learning (ECML'95), volume 912 of LNCS, page 92--106. Springer-Verlag, (1995)Abstract
When specializing a recursive predicate in order to exclude a set of negative examples without excluding a set of positive examples, it may not be possible to specialize or remove any of the clauses in a refutation of a negative example without excluding any positive examples. A previously proposed solution to this problem is to apply program transformation in order to obtain non-recursive target predicates from recursive ones. However, the application of this method prevents recursive specializations from being found. In this work, we present the algorithm SPECTRE II which is not limited to specializing non-recursive predicates. The key idea upon which the algorithm is based is that it is not enough to specialize or remove clauses in refutations of negative examples in order to obtain correct specializations, but it is sometimes necessary to specialize clauses that appear only in refutations of positive examples. In contrast to its predecessor SPECTRE, the new algorithm is not limited to specializing clauses defining one predicate only, but may specialize clauses defining multiple predicates. Furthermore, the positive and negative examples are no longer required to be instances of the same predicate. It is proven that the algorithm produces a correct specialization when all positive examples are logical consequences of the original program, there is a finite number of derivations of positive and negative examples and when no positive and negative examples have the same sequence of input clauses in their refutations.