Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability (2016), p. 374
by Bjørdal, Frode

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Caption

The cube of opposition for deontic-agentive modalities and directives

Logic

Aristotelian family

Buridan Sigma-4

Boolean complexity

6

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Cube (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

deontic logic

Edge description

Style

Diagram is colored

Yes

Diagram is embellished

No

Additional notes

O stands for 'obligatory'; P abbreviates ~O~.

B stands for 'it is brought about that'; the inverted B abbreviates ~B~.

(Cf. p. 373)