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 
.
