The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

Research Paper #910

Title:On Automating Diagrammatic Proofs of Arithmetic Arguments
Authors:Jamnik,M; Bundy,A; Green,I
Date:May 1998
Presented:Extended version of work published in the Proceedings of International Joint Conference on AI, 1997
Keywords:automated reasoning, diagrammatic reasoning
Abstract:Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an inuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the "inference steps" of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive omega-rule provides the mathematical basisfor this step from schematic proofs to theoremhood. In this way we avoid the difficulty of treating a general case in a diagram. One method of confirming that the abstraction of the schematic proofs in the meta-theory of diagrams. These ideas have been implemented in the system, called DIAMOND, which is presented here.

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