File:Relation 1111 1111 (cubic matrix).png

This file shows a 16×16×16 "logical tensor" representing a 3-ary Boolean relation. (white 0, red 1)

In the following example calculation the 3-ary relations are represented by their logical tensor,
their Venn diagrams and cubes dual to the Venn diagrams.

As the used operation is and the resulting tensor shows all ones that are both in the fist and in the second input.

${\displaystyle A\subseteq B}$	${\displaystyle \land ~}$	${\displaystyle B\subseteq C}$	${\displaystyle \Leftrightarrow }$	${\displaystyle A\subseteq B\subseteq C}$
1011 1011	${\displaystyle \land ~}$	1100 1111	${\displaystyle \Leftrightarrow ~}$	1000 1011

The dimension 3 is necesseary because 3-ary relations are to be represented.
The 2⁴=16 is a random power of two. Tensors like this one represent the relations in a four element universe.

 

This image was created with POV-Ray.

 

This file was uploaded with Commonist.