Schema conversion needs a measure
of the information capacity preserved by the conversion. Thus,
converting a schema 
in data model 
to schema 
in
data model 
(
and 
can be the same or different
data models), involves defining a data mapping (converter)
that can transform instances of 
into instances of 
.
Informally, 
is said to preserve the information capacity of 
if the data mapping associated with the conversion of 
into
transforms instances of 
into instances of 
without loss of information.
Information Capacity Preserving Schema Conversion.
Let 
be a schema in data model 
and let 
be a schema in data model 
.
preserves the information capacity of 
if
such that
converts (maps) a consistent state of 
into a consistent state of 
;
such that
converts a consistent state of 
into a consistent states of 
;
followed by 
is the identity
on the set of all consistent states of 
.
If 
is also total and the composition
of 
followed by 
is the identity on the set of all
consistent states of 
,
then 
and 
have equivalent information capacity.
Information capacity has been used extensively to characterize the correctness of schema conversions within the same data model (e.g., relational database schema normalization transformations) or between different data models. The degree of information capacity preservation depends on the goal of schema conversion [15]:
is used only as a view for querying a database
specified using schema 
then the conversion of 
into 
does not need to preserve the information capacity of 
;
however, if 
is also used for querying a database specified using
schema 
then 
and 
must have equivalent
information capacity;
is used for viewing (e.g., browsing)
an entire database specified using schema
then 
must have at least the information capacity of 
;
is used for updating a database specified using schema
then 
and 
must have equivalent information capacity.