From Euler Diagrams to Aristotelian Diagrams (2022), p. 289
by Demey, Lorenz; Smessaert, Hans

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Caption

(a) Euler diagram for the bi-implication between $A$ and $B$. (b) The corresponding classical square of opposition. (c–h) Highlighting the six relations among $A$, $B$, $\overline{A}$ and $\overline{B}$ in the Euler diagram (note: the four CD are Aristotelian relations, but the two BI are not).

Logic

Aristotelian family

A Single PCD

Boolean complexity

2

Number of labels per vertex (at most)

2

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

Digon (regular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By central symmetry

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

none

Label type

symbolic

Symbolic field

mathematics

Contains partial formulas or symbols

No

Mathematical branch

set theory

Edge description

Contains definitions of relations

No

Form

solid lines

Has arrowheads

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

Boolean closed

;

Leuven