Structures of Opposition and Comparisons: Boolean and Gradual Cases (2020), p. 128
by Dubois, Didier; Prade, Henri; Rico, Agnès

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Caption

Moretti’s cube of opposition induced by four disjoint sets (A, E, A', E')

Logic

Aristotelian family

Moretti-Pellissier Sigma-4

Boolean complexity

5

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 the Boolean complexity 5 of this diagram, cf.: "It is worth noticing that is not required that $A$, $E$, $A'$, $E'$ make a partition, indeed there is no requirement on the set $A \cup E \cup A' \cup E'$, i.e., $T = A \cap E \cap A' \cap E'$ is not necessarily empty." (p. 127).