In propositional logic I know that if I have a set of atomic formulas $S=\{A_1, . . . ,A_n \}$
That an assignment $A$ of $S$, designates truth values to each of the atomic formula in $S$,
But is there some kind of generalization or extension of this word 'assignment' in predicate logic, like say I have the propositional function,
$P:(\text{X likes Y})$
And I wanted to assign values to the propositional variables ${x,y}$.
What would I call this assignment of variables?
One term that is used is valuation. It comes up in one of the standard ways to define what is meant by a sentence of the language $L$ to be true in a particular $L$-structure $M$. Formally, a valuation is a function from the set of variable symbols to the underlying set of $M$.