Completeness (knowledge bases)

The term completeness as applied to knowledge bases refers to two different concepts.

Formal logic

In formal logic, a knowledge base KB is complete if there is no formula α such that KB ⊭ α and KB ⊭ ¬α.
Example of knowledge base with incomplete knowledge:
KB :=
Then we have KB ⊭ A and KB ⊭ ¬A.
In some cases, a consistent knowledge base can be made complete with the closed world assumption—that is, adding all not-entailed literals as negations to the knowledge base. In the above example though, this would not work because it would make the knowledge base inconsistent:
KB' =
In the case where KB :=, KB ⊭ P and KB ⊭ ¬P, so, with the closed world assumption, KB' =, where KB' ⊨ ¬P.

Data management

In data management, completeness is metaknowledge that can be asserted for parts of the KB via completeness assertions.
As example, a knowledge base may contain complete information for predicates R and S, while nothing is asserted for predicate T. Then consider the following queries:
Q1 :- R, S
Q2 :- R, T
For Query 1, the knowledge base would return a complete answer, as only predicates that are themselves complete are intersected. For Query 2, no such conclusion could be made, as predicate T is potentially incomplete.