The Closed World Assumption
The Closed World Assumption (Reiter, 1978, 1984), or CWA, asserts that if an otherwise valid tuple does not appear in the body of a relation, then the proposition representing that tuple must be false. In other words, the assumption is made that facts not known to be true in a relational database are false (Minker, 1996). This was the most important of three assumptions put forth by Reiter. The others are: the Unique Name Assumption, which states that any item in a database has a unique name and, further, that objects with different names are not the same; and the Domain Closure Assumption, which states that there are no objects other than those within the database. Two closely related rules are the Completed Database Rule and the Negation As Finite Failure Rule, both introduced by Clark (1978).
The CWA has become one of the fundamental principles of relational database theory.
In symbolic logic, such an assertion is called a completion axiom. It follows that a relation contains all of, and only those, tuples whose corresponding propositions are true. In other words, a relation body contains only those tuples that satisfy the completion axiom for its relvar. By generalization, the complete set of completion axioms for a given database defines its CWA, and the set of all tuples in a given database must also satisfy its CWA.
The following Venn diagram illustrates this point:
Note that, by the definition of the CWA, the sets of false and true propositions for a database do not intersect. See “The Closed World Assumption Revisited” on page 677 for an application of the CWA to missing information in relational databases and the paradox that nulls present to the definition of a well-formed completion axiom.