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Leonardi.DB
a logical geometry project

Why the Hexagon of Opposition is Really a Triangle: Logical Structures as Geometric Shapes (2024), p. 122
by Milstein, Ori

Copyright according to our policy

Caption

A triangular dipyramid associated with the modal logic KD. Also fit for representing KD45, in which case all modalities are included in the decorations. Notice the triangle of opposition at the center, extended by $p$ and $\neg p$ from both sides

Logic

Number of labels per vertex (at most)
1
Errors in the diagram
No

Geometry

Shape
Triangular Bipyramid (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
By central symmetry

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
spherical
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
No
Logical system
propositional logic

Edge description

Contains definitions of relations
No
Form
solid lines
Has arrowheads
No
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
No
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
No
Logical system
propositional logic

Style

Diagram is colored
No
Diagram is embellished
No
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