Logic programming with sequent systems

Abstract

The computational interest of SLD-resolution comes from its goal oriented strategy. One step of the computation consists in replacing the current goal (deterministically selected within the resolvent) by the body of a Horn clause (non deterministically selected in the program). This leads to a purely sequential computational model, where the whole computation is represented as a sequence of resolvents. We propose here an extension of Prolog in which the program clauses have multiple heads and which, at the same time, processes multiple current goals in parallel. The resulting computational model is well adapted to the implementation of concurrent systems, especially reactive systems where the computation is viewed as a perpetual interaction between the user(s) and the system. The natural framework for the description of our extension of Prolog is Linear Logic. However, we show here that the sequent system of propositional Classical Logic already contains the necessary tools for our purpose, especially the cut rule together with a Cut normalisation theorem. Further normalisation procedures (concerning the structural rules — Contraction, Weakening and Exchange — and directly inspired by Linear Logic) are required in Classical Logic to obtain the operational system that we propose.