Fuzzy Syllogisms, Numerical Square, Triangle of Contraries, Inter-bivalence (2012), p. 248
by Cavaliere, Ferdinando

Copyright according to our policy

Caption

Double triangle and 7 cases

Logic

Aristotelian family

Non-Sigma

Boolean complexity

7

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Rectangle (irregular)

Colinearity range

0–1

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

N.A.

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

Yes

Form

none

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

No

Logical system

syllogistics

Edge description

Style

Diagram is colored

Yes

Diagram is embellished

No

Additional notes

A-E-Y constitutes a contrariety triangle; its negation closure is a JSB sigma-3.

X-J-W constitutes a contrariety triangle; its negation closure is another JSB sigma-3.

The negation closure of the entire diagram (A,E,Y,X,J,W) consists of these two JSB sigma-3s, which will be a sigma-6 diagram.