Journal of Logic, Language and Information

, Volume 8, Issue 3, pp 297-321

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

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 ω-rule 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 meta-theory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here.

automated reasoning diagrammatic reasoning theorem proving