# Computing the maximal Boolean complexity of families of Aristotelian diagrams (2018), p. 1330

by Demey, Lorenz

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### Caption

- (a) Classical square in $\mathsf{KD}$, (b) degenerate square for the same fragment in $\mathsf{K}$, (c) JSB hexagon in $\mathsf{KD}$ and $\mathsf{K}$.

- Aristotelian family
- Jacoby-Sesmat-BlanchÃ© Sigma-3
- Boolean complexity
- 3â€“4
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Hexagon (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry

### Logic

### Geometry

- 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
- 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

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- Leuven

### Style

### Additional notes

- In $\mathsf{KD}$ this diagram has Boolean complexity 3 and is Boolean closed.

In $\mathsf{K}$ this diagram has Boolean complexity 4 and is not Boolean closed.