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Leonardi.DB
a logical geometry project # Logical Conversions (2017), p. 199 by Dekker, Paul ### Logic

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

### Geometry

Shape
Triangular Prism (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
By some other geometric feature

### Vertex description

Conceptual info
Yes
Mnemonic support (AEIO, purpurea ...)
Yes
Form
none
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
syllogistics

### Edge description

Contains definitions of relations
No
Form
solid lines
,
none
No
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
No
Label type
none

### Style

Diagram is colored
No
Diagram is embellished
No

AäB = A'eB = $\forall x(\neg Ax \to \neg Bx)$
AöB = A'iB = $\exists x(\neg Ax \wedge Bx)$

(Cf. p. 196.)

ItVR = immune to verbal restriction
AtVR = allergic to verbal restriction

(Cf. p. 199.)

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