User:Skittleys/Hierarchy test

Tests for formal logic formulae to be used in the hierarchy article:

A hierarchy can also be described using formal logic:


 * $$ \forall (a,b) \in \mathbf{X}^2 \iff (a \ge b) \lor (a \le b) \lor (x/x \ge a \land x \ge b) = \emptyset $$


 * where $$ \mathbf{X} $$ is a poset.

This formula can be simplified to:


 * $$ a \lor b = \begin{cases}

a, & \mbox{if }a \ge b \\ b, & \mbox{if }b \ge a \\ \mathbf{I}, & \mbox{otherwise} \end{cases}$$


 * where $$\mathbf{I}$$ is the (identity matrix? unit interval?).

source: http://books.google.ca/books?id=G7xHcr10zYwC&pg=PA406&dq=hierarchy+poset#v=onepage&q=hierarchy%20poset&f=false