Lgd

The first assumption is that in the case where the background is opaque (i.e. ${\alpha }_b=1$), the over operator represents the convex combination of $a$ and $b$: $C_o={\alpha }_a{C}_a+(1-{\alpha }_a)C_b$

The second assumption is that the operator must respect the associative rule: $(a\odot b)\odot c=a\odot (b\odot c)$