Completeness (knowledge bases)
Encyclopedia
A knowledge base
Knowledge base
A knowledge base is a special kind of database for knowledge management. A Knowledge Base provides a means for information to be collected, organised, shared, searched and utilised.-Types:...

 KB is complete if there is no formular 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, you can make a consistent knowledge base complete with the closed world assumption
Closed world assumption
The closed world assumption is the presumption that what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed world assumption is the open world assumption , stating that lack of knowledge...

 - 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 you have KB := { P(a), Q(a), Q(b) }, you have KB ⊭ P(b) and KB ⊭ ¬P(b), so with the closed world assumption you would get KB' = { P(a), ¬P(b), Q(a), Q(b) } where you have KB' ⊨ ¬P(b).

See also:
  • Vivid knowledge
    Vivid knowledge
    Vivid knowledge refers to a specific kind of knowledge representation.The idea of a vivid knowledge base is to get an interpretation mostly straightforward out of it – it implies the interpretation...

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