. We propose a computational model for analogy solving based on a topological formalism of representation. The source and the target analogs are represented as simplexes and the analogy solving is modeled as a topological deformation of these simplexes along a polygonal chain and according to some constraints. We apply this framework to the resolution of IQ-tests typically presented as "given A, B and C, find D such that A is to B what C is to D". 1 Introduction In this paper, we present a topological framework for knowledge representation based on the concept of simplicial complex. We present then the ESQIMO system which is the application of this framework to an analogy solving problem. The underlying idea developed here is that spatial relationships and more precisely topological relationships such as neighbor, border, dimension, obstruction, deformation, separabitily, path, etc, enable the building and structuration of knowledge representation. More precisely, we explore the possi...

We propose to model some diagrammatic reasoning tasks with a topological framework. We are not interested in reasoning on diagrams but in reasoning on a problem with a diagrammatic representation. A diagrammatic representation is formalised with topological objects, and the reasoning processed on it is modeled with topological operations. We present here three applications to illustrate the idea that combinatorial algebraic topology is an adequate and unifying framework to specify and analyse diagrammatic representations and diagrammatic reasoning. The first application presented is a categorisation problem, the second concerns hierarchy structuring, and the third is the ESQIMO system for solving analogies in unsupervised IQ-tests. Introduction Diagrammatic reasoning is a field of research investigating the use of spatial relations for knowledge processing. This includes knowledge representations, retrieval processing, inference making, etc. Several issues are addressed in these acti...

this paper, we address the problem of names and name capture on its own by designing, through the use of three operators, a complete and consistent mechanism of name capture for a declarative framework. We perceive expressions with free names as incomplete expressions which will be dynamically completed by a name capture mechanism. The formalism allows the denition of rst-class environments (which can be the result of a computation). We apply this mechanism to model distributed incremental program construction and to dene an object oriented programming style in a declarative language

8 ½, an experimental language combining features of collection and stream oriented languages...