# Structures of Opposition and Comparisons: Boolean and Gradual Cases (2020), p. 131

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

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### Caption

- Graded version of Moretti’s cube of opposition induced by four numbers ($\alpha + \epsilon + \epsilon' + \alpha' \leq 1$)

- Aristotelian family
- Moretti-Pellissier Sigma-4
- Boolean complexity
- 4–5
- 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
- logic
- Contains partial formulas or symbols
- No
- Logical system
- fuzzy logic

### Vertex description

### Edge description

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

### Style

### Additional notes

- Regarding the Boolean complexity of this diagram

(i) in the caption of the figure it is stated that $\alpha + \epsilon + \epsilon' + \alpha' \leq 1$, which leaves open Boolean complexities 4 (cf. = 1) as well as 5 (cf. < 1)

(ii) later on p. 131, it is stated that $\alpha + \epsilon + \epsilon' + \alpha' = 1$, which corresponds to Boolean complexity 4