Constructing predicate mappings for Goal-Dependent Abstraction

Abstract

This paper is concerned with an abstraction for SLD-refutation. In most studies on abstraction, any goal is proved with a fixed abstraction neglecting differences of goals. On the other hand, we propose a new framework of Goal-Dependent Abstraction in which an appropriate abstraction can be selected according to each goal to be proved. Towards Goal-Dependent Abstraction, this paper tries to construct an appropriate abstraction for a given goal. The appropriateness is defined in terms of Upward-Property and Downward-Property. Our abstraction is based on predicate mapping. Given a goal, candidate predicate mappings are generated and tested in their appropriateness. To find appropriate abstractions efficiently, we present a property to reduce the computational cost of candidate generation. The numbers of pruned candidates are evaluated in both of the best and worst cases. Some experimental results show that many useless candidates can be pruned with the property and constructed abstractions fit our intuition.