# Von deontischen Quadraten - Kuben - Hyperkuben (2012), p. 79

by Philipps, Lothar

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### Caption

- Deontischer Hyperkubus 1

- Aristotelian family
- Sigma-8 Graph
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Three Dimensional Shape (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 4
- Representation of contradiction
- By some other geometric feature

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Label type
- linguistic
- Contains definitions of relations
- No
- Form
- solid lines
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- No
- Label type
- none

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- composed operator duality

### Style

### Additional notes

- A visual variant of this diagram appears on p. 80 of the same paper (with the caption 'Hyperkubus 2').

The formulas in this diagram follow the composed operator duality pattern "deontic operator - quantifier - quantifier" and thus have 4 negation positions (external, intermediate 1, intermediate 2, internal), yielding 2^4 = 16 formulas.