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Leonardi.DB
a logical geometry project

From the Square to Octahedra (2017), p. 269
by García-Cruz, José David

Caption

Traditional 2PH

Logic

Aristotelian family
Keynes-Johnson Sigma-4
Boolean complexity
7
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Hexagonal 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 ...)
Yes
Form
none
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
syllogistics

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
Yes
Diagram is embellished
No
Tags
subject negation
;
generalized Post duality

Additional notes

Aab = all a are b
Eab = no a are b
Iab = some a are b (mistakenly displayed as Lab in the diagram)
Oab = some a are not b
Rab = all non-a are non-b = all b are a
Sab = no non-a are non-b = all non-a are b
Tab = some non-a are non-b
Uab = some non-a are not non-b = some non-a are b

(Cf. p. 254 and p. 257.)

Under the assumption of existential import, this diagram is a Keynes-Johnson sigma-4 (Boolean complexity 7).

If we would make the additional assumption of 'differential import' (cf. Dekker 2015), this diagram would be a Moretti sigma-4 (Boolean complexity 5).
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