Heterogeneous Reasoning in Real Arithmetic

Diagrams often complement sentential proofs in mathematics. However, diagrams are rarely used as standalone reasoning tools. Thus we propose to integrate diagrammatic reasoning with an existing sentential theorem prover, thus enabling so-called heterogeneous reasoning, particularly in real arithmetic. We will study a set of diagrammatic proof examples from which we will construct a diagrammatic language, inference rules and communication procedures between the diagrammatic and sentential reasoners. The resulting framework will allow the use of diagrammatic proof steps in the same way as the sentential ones, all within the same attempt to construct a proof.