# Graded Structures of Opposition in Fuzzy Natural Logic (2020), p. 502

by Murinová, Petra

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### Caption

- Moretti’s-cube of opposition

- 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 ...)
- Yes
- Form
- none
- Label type
- symbolic
- Symbolic field
- logic
- Contains partial formulas or symbols
- Yes
- Logical system
- syllogistics
- Contains definitions of relations
- No
- Form
- dotted lines ,
- solid lines ,
- none ,
- dashed lines
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- No
- Label type
- none

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- subject negation ;
- generalized Post duality

### Style

### Additional notes

- $A = \forall x(Bx \to Ax)$

$E = \forall x(Bx \to \neg Ax)$

$I = \exists x(Bx \wedge Ax)$

$O = \exists x(Bx \wedge \neg Ax)$

$a = \forall x(\neg Bx \to \neg Ax)$

$e = \forall x(\neg Bx \to Ax)$

$i = \exists x(\neg Bx \wedge \neg Ax)$

$o = \exists x(\neg Bx \wedge Ax)$

This diagram is a Moretti sigma-4 (with Boolean complexity 5), rather than a Keynes-Johnson sigma-4 (with Boolean complexity 7), because the following constraint is imposed: $(A \vee E) \to (i \wedge o)$.

(Cf. p. 502.)