You're using an ancient browser to surf the modern web. Please update to the latest version (and don't use Internet Explorer!).

Leonardi.DB
a logical geometry project

# Logical Extensions of Aristotle's Square (2008), p. 179 by Luzeaux, Dominique; Sallantin, Jean; Dartnell, Christopher

### 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
No
Errors in the diagram
No

### Geometry

Shape
Triangular Prism (irregular)
Colinearity range
0–1
Coplanarity range
0
Cospatiality range
0
By some other geometric feature

### Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
generic placeholders

### Style

Diagram is colored
No
Diagram is embellished
No

Each $B^i$ is equivalent to either $A^i$ above it or $C^i$ below it. Two of the $B$'s are equivalent to their corresponding $A$'s above, while the remaining third $B$ is equivalent to its corresponding $C$ below. After all, if $B^i \equiv A^i$ and $B^j \equiv A^j$, then $B^k \equiv \neg B^i \wedge \neg B^j \equiv \neg A^i \wedge \neg A^j \equiv C^k$.