The term completeness as applied to
knowledge bases
A knowledge base (KB) is a technology used to store complex structured and unstructured information used by a computer system. The initial use of the term was in connection with expert systems, which were the first knowledge-based systems.
Ori ...
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 The closed-world assumption (CWA), in a formal system of logic used for knowledge representation, is the presumption that a statement that is true is also known to be true. Therefore, conversely, what is not currently known to be true, is false. Th ...
—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(b) and KB ⊭ ¬P(b), so, with the closed world assumption, KB' = , where KB' ⊨ ¬P(b).
Data management
In data management, completeness is
metaknowledge
Meta-knowledge or metaknowledge is knowledge about knowledge.
Some authors divide meta-knowledge into orders:
* ''zero order meta-knowledge'' is knowledge whose domain is not knowledge (and hence zero order meta-knowledge is not meta-knowledge ''p ...
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 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 certa ...
*
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. Thus, any query to such a knowledge base ...
References
Knowledge representation
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