A Proposal for Automating Diagrammatic Reasoning in Continuous Domains
This paper presents one approach to the formalisation of diagrammatic proofs as an alternative to algebraic logic. An idea of ‘generic diagrams’ is developed whereby one diagram (or rather, one sequence of diagrams) can be used to prove many instances of a theorem. This allows the extension of Jamnik’s ideas in the Diamond system to continuous domains. The domain is restricted to non-recursive proofs in real analysis whose statement and proof have a strong geometric component. The aim is to develop a system of diagrams and redraw rules to allow a mechanised construction of sequences of diagrams constituting a proof. This approach involves creating a diagrammatic theory. The method is justified formally by (a) a diagrammatic axiomatisation, and (b) an appeal to analysis, viewing the diagram as an object inℝ2. The idea is to then establish an isomorphism between diagrams acted on by redraw rules and instances of a theorem acted on by rewrite rules. We aim to implement these ideas in an interactive prover entitled Rap (the Real Analysis Prover).
KeywordsTarget Domain Diagrammatic Theory Real Analysis Continuous Domain Algebraic Logic
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