• Source: 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:

Q1 :- R(x), S(x)
Q2 :- R(x), T(x)

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.




See also


Certain answer
Vivid knowledge




References

Kata Kunci Pencarian:

• Completeness (knowledge bases)
• Completeness
• Commonsense knowledge (artificial intelligence)
• Completeness (order theory)
• Zero-knowledge proof
• Knowledge representation and reasoning
• Alkali
• Closed-world assumption
• French and Raven's bases of power
• Outline of knowledge