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Leonardi.DB
a logical geometry project

"Logical Lantern": Analogue of the Square of Opposition for Propositions in V.I. Markin’s Universal Language for Traditional Positive Syllogistic Theories (2024), p. 43
by Cherkashina, Oksana

Caption

A variation of Blanché hexagon using the universal language for traditional positive syllogistic theories. (Here some of the lines have different meaning than in the previous scheme.) Thick lines show contradiction, dashed lines – contrariety, double lines – subcontrariety, arrows – subalternation

Logic

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

Geometry

Shape
Hexagon (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
circular
Label type
symbolic
Symbolic field
mathematics
Mathematical branch
set theory

Edge description

Contains definitions of relations
No
Form
bold solid lines
,
solid lines
,
dashed lines
,
double 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

Additional notes

This diagram is decorated with Pellissier's "setting" technique, which is equivalent to bitstring semantics. In particular, $\wp(\{1,2,3,4,5\})$ corresponds to bitstrings of length 5.
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