Generating readable proofs: a heuristic approach to theorum proving with spider diagrams

Abstract

An important aim of diagrammatic reasoning is to make it easier for people to create and understand logical arguments. We have worked on spider diagrams, which visually express logical statements. Ideally, automatically generated proofs should be short and easy to understand. An existing proof generator for spider diagrams successfully writes proofs, but they can be long and unwieldy. In this paper, we present a new approach to proof writing in diagrammatic systems, which is guaranteed to find shortest proofs and can be extended to incorporate other readability criteria. We apply the A* algorithm and develop an admissible heuristic function to guide automatic proof construction. We demonstrate the effectiveness of the heuristic used. The work has been implemented as part of a spider diagram reasoning tool.