Hypercube algebra: a diagrammatic and sentential notation to support inferences in logic

Abstract : Motivation - Our objective was to design a Boolean algebra allowing both a diagrammatic and sentential representation of logical propositions in an intuitive manner. The purpose of this notation is to support inferential activity without heavy deductive procedure to follow. Research approach - This research is founded on the notions of logical space proposed by Wittgenstein and of hypercube proposed by Pólya. Findings/Design - Complex propositions in propositional logic can be depicted by hypercube within a coordinate system, and by sequences of lexical symbols allowing operations on hypercube with more than three dimensions. Research limitations/Implications - Empirical studies are now required to validate the intuitiveness of this notation. Its scope of application must also be delimited. Originality/Value - Contrary to classical diagrammatic notations based on Euler topological diagrams in logic, the hypercube algebra involves a coordinate-based representation combining diagrams and lexical symbols. This is a new form of notation. Take away message - Rather than the format, the important variables in designing a representational system are those specifying the cognitive activity induced, e.g. straightforward inferences, abstraction level of symbols.
Type de document :
Communication dans un congrès
Phil and Susan Turner. European Conference on Cognitive Ergonomics, Aug 2012, Edinburgh, United Kingdom. 2012
Liste complète des métadonnées

Littérature citée [28 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00722696
Contributeur : Thierry Morineau <>
Soumis le : vendredi 3 août 2012 - 11:58:32
Dernière modification le : mercredi 29 novembre 2017 - 16:51:36
Document(s) archivé(s) le : dimanche 4 novembre 2012 - 03:40:08

Fichier

TM_ECCE2012_communication.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00722696, version 1

Collections

Citation

Thierry Morineau. Hypercube algebra: a diagrammatic and sentential notation to support inferences in logic. Phil and Susan Turner. European Conference on Cognitive Ergonomics, Aug 2012, Edinburgh, United Kingdom. 2012. 〈hal-00722696〉

Partager

Métriques

Consultations de la notice

158

Téléchargements de fichiers

155