Aristotelian and Duality Relations Beyond the Square of Opposition (2018), p. 646
by Demey, Lorenz; Smessaert, Hans

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Caption

(a) Aristotelian relations and (b) duality relations in the modal JSB hexagon.

Logic

Aristotelian family

Jacoby-Sesmat-Blanché Sigma-3

Boolean complexity

3

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

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 ...)

No

Form

none

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

No

Logical system

modal logic

Edge description

Contains definitions of relations

No

Form

solid lines

,

none

Has arrowheads

No

Overlap

No

Curved

Yes

Hooked

No

As wide as vertices

No

Contains text

Yes

Label type

linguistic

Language

English

Contains partial sentences or single words

Yes

Contain abbreviations

Yes

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Boolean closed

;

Leuven

;

duality