Leonardi.DB
a logical geometry project

Structures of Opposition and Comparisons: Boolean and Gradual Cases (2020), p. 130
by Dubois, Didier; Prade, Henri; Rico, Agnès

Caption

Moretti’s cube of opposition with similarity indices

Logic

Aristotelian family
Moretti-Pellissier Sigma-4
Boolean complexity
4
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 central symmetry

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
symbolic
Symbolic field
mathematics
Contains partial formulas or symbols
No
Mathematical branch
set theory

Edge description

Style

Diagram is colored
No
Diagram is embellished
No

Additional notes

Regarding Boolean complexity 4: cf. "Thus XYX \cap Y, XY\overline{X} \cap Y, XYX \cap \overline{Y}, XY\overline{X} \cap \overline{Y} form a quadri-partition of the set UU of objects" (p. 130).
↑ Back to top ↑