LUW May 18: Logical Diagrams, Visualization Criteria and Boolean Algebras by Roland Bolz
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ISHPSS
May 17, 2022, 5:31:02 AM5/17/22
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From: Jean-yves Beziau <bezi...@gmail.com>
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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