title: Completeness (knowledge bases)
text: # 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 := { A ∨ B }
  
  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' = { A ∨ B, ¬A, ¬B }
  
  In the case where KB := { P(a), Q(a), Q(b) }, KB ⊭ P(b) and KB ⊭ ¬P(b), so, with the closed world assumption, KB' = { P(a), ¬P(b), Q(a), Q(b) }, where KB' ⊨ ¬P(b).
  
  ## 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:
  
  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.
  
  