Condition Graphs

A connection graph represents resolvability in a set of clauses explicitly. The corresponding connection graph proof procedure has the deeciency that the graphs may grow, becoming impractical to handle. We present a novel proof procedure for condition graphs, which is a reenement of connection graphs. Our idea is to control the growth of the graph by recognizing tests in clauses and translating them to restrictions on the resolvability of links. A link is not selected for resolution unless all its associated tests have been determined to be true. The condition graph proof procedure exploits the inherent parallelism in logic programs. We present a parallel logic programming language with appealing theoretical properties, which is executed eeciently using the condition graph proof procedure. An abstract parallel machine for the language is deened. A realization of the machine on the Connection Machine, a massively parallel computer, is outlined. 1. INTRODUCTION Our goal is to eeciently execute programs in an expressive logic programming language. One way is to make use of the inherent parallelism in logic programs. For this purpose we introduce condition graphs and an associated proof procedure. Theorems for basic theoretical properties of the proof procedure are presented. Only informal proofs are given, to keep this a short paper. We suggest a language, Uplog, to be the source for the condition graphs, although other languages could be considered as well, with minor modiication of the proof procedure. Throughout the work, a primary consideration has been the possibility to implement the system on a massively parallel computer, such as the Connection Machine.* Section 2 gives a brief introduction to connection graphs. Section 3 deenes condition graphs and the condition graph proof procedure. The Uplog language is introduced in section 4. The Condition Graph Inference Machine is deened in section 5. Finally section 6 contains a realization of the Condition Graph Inference Machine on the Connection Machine.