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The term completeness as applied to knowledge bases refers to two different concepts.
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The term completeness as applied to knowledge bases refers to two different concepts.
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).
In data management, completeness is metaknowledge that can be asserted for parts of the KB via completeness assertions. [1] [2]
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.
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Prolog is a logic programming language associated with artificial intelligence and computational linguistics.
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In database theory and knowledge representation, the one of the certain answers is the set of answers to a given query consisting of the intersection of all the complete databases that are consistent with a given knowledge base. The notion of certain answer, investigated in database theory since the 1970s, is indeed defined in the context of open world assumption, where the given knowledge base is assumed to be incomplete.
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