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schema. However, checking redundancy of entities, that is, whether two dif-
ferent entity names represent the same universe of discourse, is difficult. The
only redundancy that can be checked in a conceptual schema concerns integ-
rity constraints and some relationships.
Checking whether a given integrity constraint is redundant is a logical
inference problem. If the integrity constraint can be logically derived from
other constraints, it is redundant; otherwise, it is not. If we restrict the set of
constraints to those usually represented in a conceptual schemacardinali-
ties, unicity of keys, functional dependencies, inclusion dependencies, and so
forthwe can use specific rules to check redundancy of each type of con-
straint. Most of the rules are the same as those used for checking consistency.
Inference rules between functional dependencies can be used to check both
their consistency and their redundancy.
For example, given the following known dependencies and independ-
encies: {A
®
B; (B,D)
®
E; (C,F)
®
G; (A,F)
¤®
G}, we can use the
same inference rules to check that (A,D)
®
E is redundant and to check
that A
C is inconsistent. More precisely, in both cases we use pseudo-
transitivity. The theorem proves for redundancy checks whether the goal can
be derived from other constraints, while the theorem proves for consistency
checks
¤®
whether
the
negation
of
the
goal
can
be
derived
from
other
constraints.
As for the consistency, an intelligent CASE tool should combine all the
known inference rules for functional dependencies, inclusion dependencies,
and cardinalities into the same theorem proof in order to check the redun-
dancy or irredundancy of a conceptual schema.
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Figure 13.10
Redundancy.
