LUW May 18: Logical Diagrams, Visualization Criteria and Boolean Algebras by Roland Bolz

jean-yves beziau beziau100 at
Mon May 16 09:41:07 EDT 2022

Logica Universalis Webinar, Wednesday May 18, 4pm CET

Speaker: Roland Bolz (Humboldt University, Berlin, Germany)
Title: Logical Diagrams, Visualization Criteria and Boolean Algebras
Abstract: This paper presents logical diagrams as attempts to visualize
facts about logical/linguistic/conceptual systems. It introduces four
criteria for assessing visualization: 1) completeness, 2) correctness, 3)
lack of distortion, and 4) legibility. It then  presents well-known
families of diagrams, based on the geometrical figures of a) the hexagon,
and b) the tetrakis hexahedron. These are usually presented as exemplary
diagrams. To understand better why they succeed so well at visualizing
logical information, they are presented as visualizations of complete
(finite) Boolean algebras. This also establishes the connection between the
combinatorial concept of partition and the logical concept of opposition
(i.e. contradiction, contrariness, and subcontrariness). Finally, the paper
suggests that the two geometrical figures in question are part of a larger
family of polytopes with deep connections to Boolean algebras.

Chapter of the book  The Exoteric Square of Opposition

Talk originally presented at the 6th SQUARE

Everybody is welcome to join:

Jean-Yves Beziau, Organizer of LUW and Editor of Studies in Universal Logic
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