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Leonardi.DB
a logical geometry project

From the Structures of Opposition Between Similarity and Dissimilarity Indicators to Logical Proportions. A General Representation Setting for Capturing Homogeneity and Heterogeneity (2017), p. 283
by Prade, Henri; Richard, Gilles

Caption

Cube of opposition

Logic

Aristotelian family
Keynes-Johnson Sigma-4
Boolean complexity
7
Number of labels per vertex (at most)
2
Equivalence between (some) labels of the same vertex
No
Analogy between (some) labels of the same vertex
No
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
linguistic
,
symbolic
Language
English
Lexical field
syllogistics
Contains partial sentences or single words
No
Contains abbreviations
Yes
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
syllogistics

Edge description

Contains definitions of relations
No
Form
dashed lines
,
none
,
dotted lines
,
double dashed lines
,
double solid lines
,
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
Yes
Diagram is embellished
No
Tags
subject negation
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