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Leonardi.DB
a logical geometry project

Boolean Subtypes of the U4 Hexagon of Opposition (2024), p. 4
by Demey, Lorenz; Erbas, Doruk Atahan

Caption

(a) Classical square of opposition for $(\mathcal{F}_\textit{cat}, \mathsf{SYL})$, (b) U4 hexagon for $(\mathcal{F}^\textit{cc}_\textit{cat}, \mathsf{SYL})$, (c) U4 hexagon for $(\mathcal{F}^\textit{cc}_\textit{cat}, \mathsf{SYL})$, together with the bitstring semantics $\beta_\textit{cc}$.

Logic

Aristotelian family
Degenerate Sigma-3 with Unconnectedness 4
Boolean complexity
5
Number of labels per vertex (at most)
2
Equivalence between (some) labels of the same vertex
No
Analogy between (some) labels of the same vertex
No
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 ...)
Yes
Form
none
Label type
symbolic
Symbolic field
bitstrings
,
logic
Contains partial formulas or symbols
No
Contains protobitstrings
No
Bitstring length
5
Logical system
syllogistics

Edge description

Contains definitions of relations
No
Form
dotted lines
,
solid lines
,
none
,
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
Leuven
;
conversion
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