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Leonardi.DB
a logical geometry project

# Not Only Barbara (2015), p. 125 by Dekker, Paul

### Logic

Aristotelian family
Non-Sigma
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
Tetrahedron (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
N.A.

### Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
linguistic
Language
English
Lexical field
deontic operators
Contains partial sentences or single words
Yes
Contains abbreviations
No

### 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

The negation closure of this diagram is (purportedly) a U4 sigma-3, because here, the assumption of 'differential import' (cf. p. 100) does not make sense. For example, consider 'must' (ä) and 'should' (a). In a JSB sigma-3, these two items should be contrary to each other, whereas in a U4 sigma-3 they should be unconnected/independent. And as a matter of fact, it is clear that they are unconnected, in particular, the following two sentences (cf. p. 125) can be true together:

Don must play.
Don should play.

These two sentences are true together in a situation where playing is both necessary and sufficient for Don to meet his requirements. This implies a violation of the 'differential import' assumption, but it constitutes perfectly imaginable situation.

The partition induces by this diagram (subject to existential, but not differential import) consists of the following five anchor formulas (cf. the Gergonne relations!):
$\bullet$ should $\wedge$ must
$\bullet$ should $\wedge$ not must
$\bullet$ may $\wedge$ not should $\wedge$ not must
$\bullet$ not should $\wedge$ must
$\bullet$ may_not