# Logical Conversions (2017), p. 196

by Dekker, Paul

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- Aristotelian family
- Jacoby-Sesmat-Blanché Sigma-3
- 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
- Triangular Prism (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By some other geometric feature

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- Yes
- Form
- none
- Label type
- symbolic
- Symbolic field
- logic
- Contains partial formulas or symbols
- No
- Logical system
- syllogistics
- Contains definitions of relations
- No
- Form
- solid lines ,
- none
- 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

- AäB = A'eB = $\forall x(\neg Ax \to \neg Bx)$

AöB = A'iB = $\exists x(\neg Ax \wedge Bx)$

(Cf. p. 196.)

This is a JSB sigma-3 (rather than a U4 sigma-3, as in Kraszewski 1956), because we assume not only existential import, but also 'differential import': "$\emptyset \neq A \neq B \neq \emptyset$" (p. 196).

The partition induced by this diagram (subject to existential as well as differential import) consists of the following four anchor formulas:

$\bullet$ AaB

$\bullet$ AiB $\wedge$ AoB $\wedge$ AäB

$\bullet$ AiB $\wedge$ AoB $\wedge$ AöB

$\bullet$ AeB