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Leonardi.DB
a logical geometry project

Not Only Barbara (2015), p. 99
by Dekker, Paul

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
Yes
Errors in the diagram
No

Geometry

Shape
Square (regular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
By some other geometric feature

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
Yes
Form
none
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
No
Logical system
syllogistics

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
No
Diagram is embellished
No
Tags
subject negation

Additional notes

This is a twisted square of opposition: the two contradiction relations are not on the diagonals of the diagram, but on the vertical edges.

AäB = A'eB = $\forall x(\neg Ax \to \neg Bx)$
AxB = A'aB = $\forall x(\neg Ax \to Bx)$
AöB = A'iB = $\exists x(\neg Ax \wedge Bx)$
AyB = A'oB = $\exists x(\neg Ax \wedge \neg Bx)$

(Cf. p. 99.)
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