# Structures of Opposition and Comparisons: Boolean and Gradual Cases (2020), p. 130

by Dubois, Didier; Prade, Henri; Rico, Agnès

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### Caption

- Moretti’s cube of opposition with similarity indices

- 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
- 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 Boolean complexity 4: cf. "Thus $X \cap Y$, $\overline{X} \cap Y$, $X \cap \overline{Y}$, $\overline{X} \cap \overline{Y}$ form a quadri-partition of the set $U$ of objects" (p. 130).