The Square of Opposition and Generalized Quantifiers (2012), p. 223
by D'Alfonso, Duilio

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Caption

On the left is showed the classical square of opposition, on the right the modern interpretation. The logical relations in the classical square involve the existential import

Logic

Aristotelian family

Classical Sigma-2

Boolean complexity

3

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Square (regular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By some other geometric feature

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

none

Label type

linguistic

Language

English

Lexical field

syllogistics

Contains partial sentences or single words

Yes

Contains abbreviations

No

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Tags

duality

Additional notes

This is a twisted square: the contradiction (external negation) relations are on the vertical edges, rather than on the diagonals.