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Leonardi.DB
a logical geometry project

Von deontischen Quadraten - Kuben - Hyperkuben (2012), p. 79
by Philipps, Lothar

Caption

Deontischer Hyperkubus 1

Logic

Aristotelian family
Sigma-8 Graph
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Three Dimensional Shape (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
4
Representation of contradiction
By some other geometric feature

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Label type
linguistic

Edge description

Contains definitions of relations
No
Form
solid lines
Has arrowheads
Yes
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
No
Label type
none

Style

Diagram is colored
No
Diagram is embellished
No
Tags
composed operator duality

Additional notes

A visual variant of this diagram appears on p. 80 of the same paper (with the caption 'Hyperkubus 2').

The formulas in this diagram follow the composed operator duality pattern "deontic operator - quantifier - quantifier" and thus have 4 negation positions (external, intermediate 1, intermediate 2, internal), yielding 2^4 = 16 formulas.
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