Suppose we treat plus as a relation taking 3 arguments.
That is, we say
plus(2,3,5) is true because 2 + 3 = 5.and so on ....
plus(2,3,4) is false because 2 + 34.
A Logic Program for plus is one that somehow expresses for any three arguments X, Y, Z the truth value of plus(X,Y,Z).