Let be a relational
system, and let
be a language which is appropriate for . Let be a well-formed formula of , and let be a valuation in . Then is written provided that one of the following holds:

1. is of the form , for some variables and of , and maps and to the same element of the structure .

2. is of the form , for some -ary predicate symbol of the language , and some variables of , and is a member of .

3. is of the form , for some formulas and of such that and .

4. is of the form , and there is an element of such that .

In this case,
is said to satisfy
with the valuation .