A rule is filter, then project

Take the handout’s first rule: the adults in a person table.

adult(Name) :- person(Name, Age), Age >= 18.

The single body atom is the table person. The comparison Age >= 18 keeps some rows, a filter σ. The head keeps only the name, column #1, a projection π:

adult := π#1( σ#2 ≥ 18( person ) )
Read it inside out: filter person down to the adult rows, then project onto the name. Columns are positional, so Age is #2.