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Leonardi.DB
a logical geometry project

# Logik im Recht. Grundlagen und Anwendungsbeispiele (2010), p. 213 by Joerden, Jan C.

### Caption

Die Beziehungen zwischen Sollen und Sein (ergänzte Version)

### Logic

Aristotelian family
Sigma-6 Graph
Boolean complexity
5
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
6
Cospatiality range
0
By central symmetry

### Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
dots
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
deontic logic
,
modal logic

### Edge description

Contains definitions of relations
No
Form
dotted lines
,
solid lines
,
none
,
dashed lines
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

The innermost hexagon consists of the alethic modalities; N = $\Box p$, U = $\Box\neg p$, K = $\Diamond p\wedge\Diamond\neg p$.
The outermost hexagon consists of the deontic modalities; G = $O p$, V = $O\neg p$, I = $P p\wedge P\neg p$.
1) N ($\Box p$)
2) G $\wedge$ K = G $\wedge$ $\neg$N ($Op \wedge \Diamond\neg p$)
3) I ($Pp \wedge P\neg p$)
4) V $\wedge$ K = V $\wedge$ $\neg$U ($O\neg p \wedge \Diamond p$)
5) U ($\Box \neg p$)