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Leonardi.DB
a logical geometry project

Algebraic Aspects of Duality Diagrams (2012), p. 302
by Demey, Lorenz

Caption

(a) The duality cube for $\mathbb{G}_8$. (b) The two squares for {I, L, M, LM}, and (c) for {I, L, RM, LRM}. (d) One of the two tetrahedra for {I, LR, RM, LM}.

Logic

Aristotelian family
Non-Sigma
Boolean complexity
4–16
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Tetrahedron (regular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
N.A.

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
generic placeholders

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
none

Style

Diagram is colored
Yes
Diagram is embellished
No
Tags
Leuven
;
subdiagram
;
composed operator duality
;
duality

Additional notes

'L', 'M' and 'R' stand for left (= external), middle and right (= internal) negation, respectively.
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