Possibility and Necessity in the Time of Peter Abelard (2022), p. 167
by Binini, Irene

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Caption

The square of oppositions for quantified modals II

Logic

Aristotelian family

Classical Sigma-2

Boolean complexity

3

Number of labels per vertex (at most)

3

Equivalence between (some) labels of the same vertex

Yes

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

Rectangle (irregular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By central symmetry

Vertex description

Conceptual info

Yes

Mnemonic support (AEIO, purpurea ...)

No

Form

rectangular

Label type

linguistic

Language

English

Lexical field

modal syllogistics

Contains partial sentences or single words

No

Contains abbreviations

No

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

Latin

Contains partial sentences or single words

Yes

Contain abbreviations

No

Style

Diagram is colored

No

Diagram is embellished

No

Tags

composed operator duality

;

duality