A family of goal directed theorem provers based on conjunction and implication: Part 1

This paper presents a family of theorem provers for classical, intuitionistic and neighbouring logics. The theorem provers are based on a formulation of these logics in terms of conjunction, implication and falsity. Computation is goal directed, and, for the special case of Horn clauses, coincides with pure Prolog computation. Our approach is generic, and, as we shall show in a subsequent paper, can be adapted to other logics, such as modal and temporal systems. The research described in this paper has been funded partially by Esprit project No. 393, 'ACORD', of the European Commission.