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Leonardi.DB
a logical geometry project

From Euler Diagrams to Aristotelian Diagrams (2022), p. 291
by Demey, Lorenz; Smessaert, Hans

Caption

(a) Euler diagram for the contradiction 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
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