We assume three pairwise disjoint sets VAR of variables, C of constants, and L of features.
Given a feature structure, a sequence of labels is used to extract a
substructure. Such sequence of
features is called a path and defined as an expression over
( 
will be used to indicate the empty path).
Constants are viewed as primitive unstructured informational elements.
A descriptor is a sequence sp, where s is either a variable
or a constant and p is a (possible empty) path.
A feature
equation (or atomic constraint) is defined as the equality
between descriptors, where 
is used as the equality symbol.
Thus atomic constraints are of the form
where 
and 
are both descriptors. An
-constraint 
is an atomic constraint or a conjunction of
-constraints, written as 
. Note that as
more atomic constraints are included, the formula describes fewer
feature structures, that is, it becomes less partial and more defined.
Thus, these descriptions allow for the structure, partiality and equationality
of information [Shieber1989]. For example, given that { 
,
} 
VAR, {syn, agr, number, person} L, and {sg,
3} C, then
is an -constraint denoting some feature structure in
which there is a substructure accessible via the path 
when the
value of the feature number is constrained to be the constant sg
and which can be accessed via the syn label of two different
substructures (denoted by the variables and ). Since, the
`agr' substructure is part of both `outer' substructures it is
also said that they share a substructure. However, for the
`agr' feature it is only required that if a number label is present its value
must be sg. If we add further atomic constraints to this
substructure we are able to express more information. For instance, if
we add the atomic constraint
we furthermore require that if the person label is present its value must be 3.