# From Analogical Proportion to Logical Proportions (2013), p. 476

by Prade, Henri; Richard, Gilles

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### Caption

- Square of homogeneous logical proportions

- Aristotelian family
- Non-Sigma
- Number of labels per vertex (at most)
- 2
- Equivalence between (some) labels of the same vertex
- No
- Analogy between (some) labels of the same vertex
- No
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Rectangle (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- N.A.

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- none
- Label type
- symbolic ,
- generic placeholders
- Symbolic field
- logic
- Contains partial formulas or symbols
- No
- Logical system
- propositional logic
- Contains definitions of relations
- No
- Form
- dotted lines ,
- solid lines ,
- double solid lines
- Has arrowheads
- No
- 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

### Style

### Additional notes

- $S_{a,b}$ is defined as $a \wedge b$.

$S'_{a,b}$ is defined as $\overline{a} \wedge \overline{b}$.

$D_{a,b}$ is defined as $a \wedge \overline{b}$.

$D'_{a,b}$ is defined as $\overline{a} \wedge b$.

(Cf. p. 476.)