Vivid knowledge refers to a specific kind of
knowledge representation
Knowledge representation and reasoning (KRR, KR&R, KR²) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks such as diagnosing a medic ...
.
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
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. ...
can be reduced to a
database
In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
-like query.
Propositional knowledge base
A
propositional
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, "meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...
knowledge base
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. ...
KB is vivid ''iff'' KB is a
complete
Complete may refer to:
Logic
* Completeness (logic)
* Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable
Mathematics
* The completeness of the real numbers, which implies ...
and
consistent
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consisten ...
set of
literals (over some vocabulary).
Such a knowledge base has the property that it as exactly one interpretation, i.e. the interpretation is unique. A check for entailment of a sentence can simply be broken down into its literals and those can be answered by a simple database-like check of KB.
First-order knowledge base
A
first-order knowledge base KB is vivid ''iff'' for some finite set of positive function-free ground literals KB
+,
: KB = KB
+ ∪ Negations ∪ DomainClosure ∪ UniqueNames,
whereby
: Negations ≔ ,
: DomainClosure ≔ ,
: UniqueNames ≔ .
All interpretations of a vivid first-order knowledge base are isomorphic.
[Knowledge Representation and Reasoning / Ronald J. Brachman, Hector J. Levesque / page 339]
See also
*
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 ...
References
Knowledge representation
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