# 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')

- 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
- Shape
- Cube (regular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry

### Logic

### Geometry

- 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

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No

### Style

### 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).