Relevant logic programming

In this paper we present a fragment of (positive) relevant logic which can be computed by a straightforward extension to SLD resolution while allowing full nesting of implications. These two requirements lead quite naturally to a fragment in which the major feature is an ambiguous 'user-level' conjunction which is interpreted intensionally in 'query' positions and extensionally in 'assertion' positions. These restrictions allow a simple and efficient extension to SLD resolution (and more particularly, the PROLOG evaluation scheme) with quite minor loss in expressive power.