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Leonardi.DB
a logical geometry project

Graded Structures of Opposition in Fuzzy Natural Logic (2020), p. 503
by Murinová, Petra

Caption

JK-cube of opposition

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
Cube (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
Yes
Logical system
syllogistics

Edge description

Contains definitions of relations
No
Form
dotted lines
,
solid lines
,
none
,
dashed 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
subject negation
;
generalized Post duality

Additional notes

$A = \forall x(Bx \to Ax)$
$E = \forall x(Bx \to \neg Ax)$
$I = \exists x(Bx \wedge Ax)$
$O = \exists x(Bx \wedge \neg Ax)$
$a = \forall x(\neg Bx \to \neg Ax)$
$e = \forall x(\neg Bx \to Ax)$
$i = \exists x(\neg Bx \wedge \neg Ax)$
$o = \exists x(\neg Bx \wedge Ax)$

(Cf. p. 502.)
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