Jean-Louis Giavitto

A Topological Framework for Modelling Diagrammatic Reasoning Tasks

In this chapter we propose to model some diagrammatic reasoning tasks within a topological framework. We only focus on problems that require a specific diagrammatic reasoning procedure to be solved rather than on reasoning on diagrams To model such cognitive tasks, we propose to represent the problem with topological objects and to model the diagrammatic operations performed on them as topological operations. The idea underlying this proposition is that combinatorial algebraic topology is an adequate and unifying framework to specify and analyse diagrammatic representations and reasoning. To illustrate such a proposal, we present here three applications of this topological framework: the first concerns a categorisation problem, the second deals with hierachy restructuring, and the last one is the ESQIMO system for simple intra-domain analogy solving in unsupervised IQ tests.