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Leonardi.DB
a logical geometry project

Aristotelian and Duality Relations Beyond the Square of Opposition (2018), p. 651
by Demey, Lorenz; Smessaert, Hans

Caption

(a) Keynes-Johnson octagon in syllogistics with subject negation - note that $\forall(A,B)$ should be read as $\textit{all A are B}$; (b) Moretti octagon in propositional logic.

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
Octagon (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
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
,
none
,
dashed lines
Has arrowheads
Yes
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
Yes
Label type
linguistic
Language
English
Contains partial sentences or single words
Yes
Contain abbreviations
Yes

Style

Diagram is colored
No
Diagram is embellished
No
Tags
subject negation
;
Leuven
;
generalized Post duality
;
duality
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