The Logic of Geometric Proof

Abstract

Logical studies of diagrammatic reasoning—indeed, mathematical reasoning in general—are typically oriented towards proof-theory. The underlying idea is that a reasoning agent computes diagrammatic objects during the execution of a reasoning task. These diagrammatic objects, in turn, are assumed to be very much like sentences. The logician accordingly attempts to specify these diagrams in terms of a recursive syntax. Subsequently, he defines a relation ⊢ between sets of diagrams in terms of several rules of inference (or between sets of sentences and/or diagrams in case of so-called heterogeneous logics). Thus, diagrammatic reasoning is seen as being essentially a form of logical derivation. This proof-theoretic approach towards diagrammatic reasoning has been worked out in some detail, but only in a limited number of cases. For example, in case of reasoning with Venn diagrams and Euler diagrams (Shin [5] and Hammer [2]).