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Leonardi.DB
a logical geometry project

Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition (2017), p. 97
by Kumova, Bora I.

Caption

n-quantified fuzzy-logical graph of opposition $^n\Omega$ with $n - 1$ fuzzy existential quantifiers and traditional relationships

Logic

Aristotelian family
Classical Sigma-2
Boolean complexity
3
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
No
Errors in the diagram
Yes

Geometry

Shape
Rectangle (irregular)
Colinearity range
0–1
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
By central symmetry

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
Yes
Form
circular
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
Yes
Hooked
No
As wide as vertices
No
Contains text
Yes
Label type
linguistic
Language
English
Contains partial sentences or single words
Yes
Contain abbreviations
No

Style

Diagram is colored
No
Diagram is embellished
No

Additional notes

Given that A is contradictory to all vertices on the right hand side (except for E), it follows that all these vertices on the right hand side (except for E) are logically equivalent to each other.

Given that E is contradictory to all vertices on the left hand side (except for A), it follows that all these vertices on the left hand side (except for A) are logically equivalent to each other.
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