Showing papers by "Henrik Boström published in 1995"

Covering vs divide-and-conquer for top-down induction of logic programs

Abstract: Covering and divide-and-conquer are two well-established search techniques for top-down induction of propositional theories. However, for top-down induction of logic programs, only covering has been formalized and used extensively. In this work, the divide-and-conquer technique is formalized as well and compared to the covering technique in a logic programming framework Covering works by repeatedly specializing an overly general hypothesis, on each iteration focusing on finding a clause with a high coverage of positive examples. Divide-and-conquer works by specializing an overly general hypothesis once, focusing on discriminating positive from negative examples. Experimental results are presented demonstrating that there are cases when more accurate hypotheses can be found by divide-and-conquer than by covering. Moreover, since covering considers the same alternatives repeatedly it tends to be less efficient than divide-and-conquer, which never considers the same alternative twice. On the other hand, covering searches a larger hypothesis space, which may result in that more compact hypotheses are found by this technique than by divide-and-conquer. Furthermore, divide-and-conquer is, in contrast to covering, not applicable to learning recursive definitions.

Specialization of recursive predicates

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.

JIGSAW: Puzzling together RUTH and SPECTRE (Extended Abstract)

Abstract: The system JIGSAW that we have presented in this work is an example of integrating independently developed techniques. Benefiting from the common logical framework of the ILP research field, we were able to extend the theory revision system RUTH. More specifically, we integrated SPECTRE's specialization operator together with the impurity measure used for formulating a preference criterion. Experimental results using the Student Loan domain and the CUP domain show that the integration effort is beneficial, and they point out the advantages (and also some caveats) concerning the use of an unfolding technique.