# The Logic of Geometric Proof

• Ron Rood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4045)

## 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]).

## Keywords

External Memory Reasoning Task Base Side Relation Symbol Geometric Proof
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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