Ancient relational logic in Scotus Erigena

Consider the general four-fold division of all things in book IV of the Periphyseon.  The relation is $C(x,y)$, $x$ creates $y$.  Then derived notions are 'creates (something)',  $C_1(x) \equiv \exists y. C(x,y)$, 'being created (by something)', $C_2(x) \equiv \exists y. C(y,x)$. Then the four categories are \[A_1(x)\equiv C_1(x)\& \sim C_2(x)\] \[A_2(x)\equiv C_1(x)\&C_2(x)\] \[A_3(x)\equiv \sim C_1(x)\& C_2(x)\] \[A_4(x)\equiv \sim C_1(x)\& \sim C_2(x)\]

In CIL we would have that $C_1$ is $log^\exists_{(0,1)} C$ and $C_2$ is $log^\exists_{(0,1)}per_{(1,2)} C$.