Decisions on CWA vs. OWA determine the understanding of the actual semantics of a conceptual expression with the same notations of concepts.
A successful formalization of natural language semantics usually cannot avoid an explicit revelation of whether the implicit logical backgrounds are based on CWA or OWA.
Negation as failure is related to the closed-world assumption, as it amounts to believing false every predicate that cannot be proved to be true.
For example, if a database contains the following table reporting editors who have worked on a given article, a query on the people not having edited the article on Formal Logic is usually expected to return "Sarah Johnson".
In the closed-world assumption, the table is assumed to be complete (it lists all editor-article relationships), and Sarah Johnson is the only editor who has not edited the article on Formal Logic.
In contrast, with the open-world assumption the table is not assumed to contain all editor-article tuples, and the answer to who has not edited the Formal Logic article is unknown.
Adding the negation of these two literals to the knowledge base leads to which is inconsistent.
In other words, this formalization of the closed-world assumption sometimes turns a consistent knowledge base into an inconsistent one.
Checking whether the original closed-world assumption introduces an inconsistency requires at most a logarithmic number of calls to an NP oracle; however, the exact complexity of this problem is not currently known.
[9] An intermediate ground between OWA and CWA is provided by the partial-closed world assumption (PCWA).
Under the PCWA, the knowledge base is generally treated under open-world semantics, yet it is possible to assert parts that should be treated under closed-world semantics, via completeness assertions.
The PCWA is especially needed for situations where the CWA is not applicable due to an open domain, yet the OWA is too credulous in allowing anything to be possibly true.