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Leonardi.DB
a logical geometry project

# Metalogical Decorations of Logical Diagrams (2016), p. 269 by Demey, Lorenz; Smessaert, Hans

### Caption

Seuren’s relations as decorations of a an ‘unconnected-4’ hexagon (no constraints) and b a weak JSB hexagon (constraint: satisfiability of the first argument)

### Logic

Aristotelian family
Jacoby-Sesmat-Blanché Sigma-3
Boolean complexity
4
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 (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
By central symmetry

### Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
symbolic
Symbolic field
metalogic
Contains partial formulas or symbols
No

### Style

Diagram is colored
No
Diagram is embellished
No
Tags
Leuven

The 'fourth' anchor formula, which makes the difference between Boolean complexities 3 and 4, is $(\textit{RI} \cup \textit{NI}) \cap (\textit{CD} \cup \textit{C} \cup \textit{SC} \cup \textit{BI} \cup \textit{LI} \cup \textit{NI}) \cap (\textit{SC} \cup \textit{NCD})$. If $\varphi$ is a tautology and $\psi$ is contingent, then $(\varphi,\psi)$ indeed stand in the relation $(\textit{RI} \cup \textit{NI}) \cap (\textit{CD} \cup \textit{C} \cup \textit{SC} \cup \textit{BI} \cup \textit{LI} \cup \textit{NI}) \cap (\textit{SC} \cup \textit{NCD})$, so the latter is not empty, and hence, the Boolean complexity of this diagram is indeed 4 (rather than 3). Also cf. Footnote 34 on p. 268.