Consistency (knowledge bases)
Encyclopedia
A knowledge base
KB is consistent iff
its negation is not a tautology
.
I.e., a knowledge base KB is inconsistent (not consistent) iff
there is no interpretation
which entails
KB.
Example of an inconsistent knowledge base:
KB := { a, ¬a }
Consistency in terms of knowledge bases is mostly the same as the natural understanding of consistency
.
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 consistent iff
IFF
IFF, Iff or iff may refer to:Technology/Science:* Identification friend or foe, an electronic radio-based identification system using transponders...
its negation is not a tautology
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...
.
I.e., a knowledge base KB is inconsistent (not consistent) iff
IFF
IFF, Iff or iff may refer to:Technology/Science:* Identification friend or foe, an electronic radio-based identification system using transponders...
there is no interpretation
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...
which entails
Entailment
In logic, entailment is a relation between a set of sentences and a sentence. Let Γ be a set of one or more sentences; let S1 be the conjunction of the elements of Γ, and let S2 be a sentence: then, Γ entails S2 if and only if S1 and not-S2 are logically inconsistent...
KB.
Example of an inconsistent knowledge base:
KB := { a, ¬a }
Consistency in terms of knowledge bases is mostly the same as the natural understanding of consistency
Consistency
Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...
.