Logical Geometries and Information in the Square of Oppositions (2014), p. 558
by Smessaert, Hans; Demey, Lorenz

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Caption

The a opposition, b Aristotelian and c implication square for $\ \{\Box p \vee \Box\neg p, \Diamond p \wedge \Diamond\neg p, p, \neg p\}$

Logic

Aristotelian family

Degenerate Sigma-2 with Unconnectedness 4

Boolean complexity

4

Number of labels per vertex (at most)

1

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

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

No

Hooked

No

As wide as vertices

No

Contains text

No

Label type

none

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Leuven