  One introduces here the natural join $P \os Q$ of graded posets $< P,\leq_P
>$ and $< Q,\leq_Q >$ with correspondingly maximal and minimal sets being
identical as expressed by ordinal sum $P\oplus Q$ apart from other definition
and due to that one arrives at a simple proof of the $M{\"{o}}bius $ function
formula for cobweb posets. We also quote the other authors explicit formulas
for the zeta matrix and its inverse for any graded posets with the finite set
of minimal elements from earlier works of the author. These formulas are based
on the formulas for cobweb posets and their $Hasse$ diagrams or graphs named
$KoDAGs$ which are interpreted as chains of binary complete or universal
relations joined by the natural join operation. Natural join of two independent
sets is therefore the ordinal sum of this trivially ordered posets represented
also by directed biclique named dibiclique and correspondingly by their $Hasse
$ diagrams or graphs named $KoDAGs$. Such cobweb posets and equivalently their
Hasse diagrams or graphs named $KoDAGs$ are also encoded by discrete
hyper-boxes and the natural join operation of such discrete hyper boxes is just
cartesian product of them accompanied with projection out of common faces. All
graded posets with no mute vertices in their $Hasse$ diagrams which means that
no vertex has indegree or outdegree equal zero are natural join of chain of
relations and may be at the same time interpreted an $n-ary$ relation, $n \in N
\cup \{\infty \}$.
