Mapping-Based Merging of Schemas - Schema Matching and Mapping - page 217

denoted S2 S1 ,and I is an equivalence preserving mapping . Informally, this

means that if S1 dominates S2 , then it is possible to retrieve all the information from
S2 by accessing S1 ; if the two are equivalent, one can get all the information from
S2 by querying S1 and one can get all the information from S1 by querying S2 .
Miller et al. show that in data integration, querying the source schemas from
the integrated views requires that the integrated schema dominates the union of
local schemas. In view integration, querying the integrated schema through the user
views requires that the union of user views dominates the integrated schema. This
notion of completeness in creating a merged or mediated schema is common, not
just for information capacity but in other generic merging algorithms such as the
specification by Buneman et al. [ 1992 ].
Ontology merging algorithms often use notions of completeness as well. How-
ever, ontology merging algorithms do not use information capacity as a basis for
comparison since ontologies often lack data. Instead, they check to ensure that all
concepts from the input ontologies appear in the merged ontology.

2.2 Instance-Level Constraints and Schema Merging

One natural question when examining work on merging schemas is how to deal
with instance-level constraints such as key constraints and foreign keys. Unfortu-
nately, as shown in Convent [ 1986 ] merging schemas is undecidable as soon as
instance-level constraints are considered, even with a very simple representation of
schemas. While Convent [ 1986 ] specifically considers relational view integration
where the integrity constraints are keys and foreign keys, it generalizes to other
schema merging areas as well.
Convent [ 1986 ] concentrates primarily on what it means to have incompatible
constraints. Informally, this means that if users are trying to integrate views, then
for each user's view, it should be possible to access those instances from the global
schema - note that this is very similar to the information capacity requirement laid
out in Sect. 2.1 by Miller et al. [ 1993 ]. Unfortunately, Convent [ 1986 ]showsthat
having incompatible constraints is undecidable even in this very basic case. Because
of this early undecidability result, schema merging works typically do not consider
instance-level constraints.

3 View Integration

As mentioned in Sect. 1 , view integration is the problem of integrating the views/
requirements that different users have of a schema, and then creating one global
schema. Typically, this global schema is one in which the data is actually stored.
Some systems may also allow the existing user views to persist, and then mappings
may be created from the user views to the global schema where the data is stored.