I was reading this article about propositional logic and transforming problems to SAT. The author often uses the following notation (taken from Dominating set section):
I don't understand what $[v,i]$ and $[w,i]$ stand for in $at\_most\_one$ and $at\_least\_one$ parts. I checked the paper twice and didn't find the part where he defines this notation. Has anyone already seen this notation and knows what it means? Why is $i$ needed? Can anybody provide example for a simple graph and for some K (2 or 3).