Rough Sets based Proofs Visualisation

Laurent Vigneron 1 Anita Wasilewska
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present here an approach we used for proving important properties of clopen topological spaces. We combine powerful theorem provers techniques (and implementations) with a graphical technique based on a graphical representation of a rough set, called Rough Diagrams. Rough Diagrams are a generalization of a classical notion of Venn Diagrams for algebra of sets to clopen topological spaces. We use them as a powerful automated technique of constructing counter-models of properties the prover has a hard time proving and the user might suspect of being false. It means we propose to add a visual tool to a prover that after some fixed number of prover deductions would start constructing a visual counter-model for a property the prover is trying to prove. A prover with the visual tool is called a visual prover. The visual prover has a completeness property: for any rough set equality we can construct its proof or its counter-model.
Mots-clés : ensembles approximants rough diagrams rough sets automated deduction démonstration automatique diagrammes
Type de document :
Communication dans un congrès
Dave, R. N. & Sudkamp, T. 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS'99, invited session on Granular Computing and Rough Sets, 1999, New York, USA, IEEE, pp.805-808, 1999
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https://hal.inria.fr/inria-00098752
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:33:10
Dernière modification le : jeudi 11 janvier 2018 - 06:19:58
Document(s) archivé(s) le : mercredi 29 mars 2017 - 12:35:03

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  • HAL Id : inria-00098752, version 1

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INRIA | LORIA | UNIV-LORRAINE

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Laurent Vigneron, Anita Wasilewska. Rough Sets based Proofs Visualisation. Dave, R. N. & Sudkamp, T. 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS'99, invited session on Granular Computing and Rough Sets, 1999, New York, USA, IEEE, pp.805-808, 1999. 〈inria-00098752〉

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