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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.
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https://hal.inria.fr/hal-00722696
Contributor : Thierry Morineau <>
Submitted on : Friday, August 3, 2012 - 11:58:32 AM
Last modification on : Wednesday, April 1, 2020 - 1:59:57 AM
Long-term archiving on: : Sunday, November 4, 2012 - 3:40:08 AM

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  • HAL Id : hal-00722696, version 1

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

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