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Une approche cognitive du langage mathématique afin d'assister les activités de manipulation de formules

Abstract : This thesis studies some specifications of a computer system which assists the mathematician. This system is inspired by the “natural” mathematician's activity. Our approach is structured according to the three following questions: I)What is the nature of the mathematical activity? II)What could we wish for such a system? III)What could we propose? We elaborate in part I some cognitive models and situate our work in complement of heuristic reasoning. We analyze the Mathematical Language and recommend the development of a linguistics of mathematics. We study some textual proofs and structure them more especially with variable granularity proof-graphs. In part II we study the apparently simple case of formulae manipulations. We try to elaborate an intelligent mathematical Assistant (Ami) which manages elementary tasks in an Integrated Mathematical Workshop. Part III starts with a state-of-the-art of Computer-Assisted Mathematics (CAMath). We propose a formulae model based on three tied structures (graphical, textual and mathematical) in order to improve formulae manipulation. We study the parsing and the generation of formulae for the case of "sigma". We then exhibit the complexity of the required knowledge to assist the mathematician's activity. Finally, we present the intended mechanisms for using mathematical identities. This thesis illustrates a more general approach: I)the analysis of a conceptual activity from a linguistic point of view II)its transcription in a “natural” activity assisted by a system III)an experimental bottom-up development of this system. In this approach that we call Intercom, the user's role is predominant as it is in the general problematic of Scientific Work Assistance. Intercom has been validated through a set of models and scenarii.
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Contributor : Gérald Moulis <>
Submitted on : Friday, February 22, 2019 - 12:34:23 PM
Last modification on : Wednesday, March 6, 2019 - 1:03:31 AM
Long-term archiving on: : Thursday, May 23, 2019 - 2:26:56 PM


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  • HAL Id : tel-02045804, version 1



Gérald Moulis. Une approche cognitive du langage mathématique afin d'assister les activités de manipulation de formules. Intelligence artificielle [cs.AI]. ISAE - Institut Supérieur de l'Aéronautique et de l'Espace, 1991. Français. ⟨tel-02045804⟩



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