Journal of Logic, Language and Information
, Volume 8, Issue 3, pp 297321
First online:
On Automating Diagrammatic Proofs of Arithmetic Arguments
 Mateja JamnikAffiliated withDivision of Informatics, University of Edinburgh
 , Alan BundyAffiliated withDivision of Informatics, University of Edinburgh
 , Ian GreenAffiliated withDivision of Informatics, University of Edinburgh
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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 intuitive 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 ωrule provides the mathematical basis for 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 proof from the proof instances is sound is proving the correctness of schematic proofs in the metatheory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here.
 Title
 On Automating Diagrammatic Proofs of Arithmetic Arguments
 Journal

Journal of Logic, Language and Information
Volume 8, Issue 3 , pp 297321
 Cover Date
 199907
 DOI
 10.1023/A:1008323427489
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 automated reasoning
 diagrammatic reasoning
 theorem proving
 Authors

 Mateja Jamnik ^{(1)}
 Alan Bundy ^{(1)}
 Ian Green ^{(1)}
 Author Affiliations

 1. Division of Informatics, University of Edinburgh, 80 South Bridge, Edinburgh, EH1 1HN, U.K. (Email