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 Béziau octagon for $\ \{\Box p, \Box\neg p, \Diamond p, \Diamond\neg p, \Box p \vee \Box\neg p, \Diamond p \wedge \Diamond\neg p, p, \neg p\}\\$ (the RI relations have not been visualized in (c) for the sake of visual clarity)

Logic

Aristotelian family

Béziau Sigma-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

Octagon (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

logic

Contains partial formulas or symbols

No

Logical system

modal logic

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Leuven

;

opposition geometry