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Leonardi.DB
a logical geometry project

Thinking Outside the Square of Opposition Box (2012), p. 86
by Jacquette, Dale

Caption

Revised and Expanded Square of Opposition with A(V) and O(V) Inversions

Logic

Aristotelian family
Degenerate Sigma-3 with Unconnectedness 4
Boolean complexity
4
Number of labels per vertex (at most)
3
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

Geometry

Shape
Hexagon (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
By central symmetry

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
Yes
Form
none
Label type
linguistic
,
symbolic
Language
English
Lexical field
syllogistics
Contains partial sentences or single words
No
Contains abbreviations
Yes
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
syllogistics
,
predicate logic

Edge description

Contains definitions of relations
No
Form
solid lines
Has arrowheads
Yes
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
Yes
Label type
linguistic
Language
English
Contains partial sentences or single words
Yes

Style

Diagram is colored
No
Diagram is embellished
No
Tags
subject negation

Additional notes

We assume that the extension of P is not the entire domain, so that A and A(V) are contraries. Furthermore, we assume that it is possible that S is the complement of P, so that E and A(V) are unconnected. Under these assumptions, this diagram is a U4 sigma3.
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