Metanormative Principles and Norm Governed Social Interaction (2014), p. 107
by Žarnić, Berislav; Bašić, Gabriela

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Caption

The hexagon of logical relations holding in standard KD deontic logic. The dotted line represents the contrariety relation, the dashed line represents contradiction, the full line represents subcontrariety, and the arrows represent subalternation (implication). Deontic concepts are expressed in natural language in the left hexagon while the right hexagon presents the corresponding formulas.

Logic

Aristotelian family

Jacoby-Sesmat-Blanché Sigma-3

Boolean complexity

3

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Hexagon (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

rounded rectangular shapes

Label type

linguistic

Language

English

Lexical field

deontic operators

Contains partial sentences or single words

Yes

Contains abbreviations

Yes

Edge description

Contains definitions of relations

No

Form

dotted lines

,

solid lines

,

dashed lines

Has arrowheads

Yes

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