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Leonardi.DB
a logical geometry project

# Not Only Barbara (2015), p. 100 by Dekker, Paul

### Logic

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

### Geometry

Shape
Cube (regular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
By some other geometric feature

### Vertex description

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

### 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
Tags
subject negation
;
generalized Post duality

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

(Cf. p. 99.)

This is a Moretti sigma-4 (rather than a Keynes-Johnson sigma-4), because we assume not only existential import, but also 'differential import': "The $\textit{differential import}$ of a proposition AuB is that A and B make a different proper distinction, i.e., $A \neq \emptyset \neq A'$, $B \neq \emptyset \neq B'$ and $A \neq B \neq A'$." (p. 100)

The partition induced by this diagram (subject to existential as well as differential import) consists of the following five anchor formulas:
$\bullet$ AaB
$\bullet$ AäB
$\bullet$ AeB
$\bullet$ AxB
$\bullet$ AiB $\wedge$ AoB $\wedge$ AöB $\wedge$ AyB