Logical Extensions of Aristotle's Square (2008), p. 171
by Luzeaux, Dominique; Sallantin, Jean; Dartnell, Christopher

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Caption

The “Boolean” tetraicosahedron.

Logic

Aristotelian family

Classical Sigma-7

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

Tetraicosahedron (irregular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By central symmetry

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

none

Label type

symbolic

Symbolic field

mathematics

Contains partial formulas or symbols

No

Mathematical branch

set theory

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Boolean closed

Additional notes

This diagram is decorated with Pellissier's "setting" technique, which is equivalent to bitstring semantics. In particular, $\wp(\{1,2,3,4\})$ corresponds to bitstrings of length 4.