Completeness (knowledge bases)
- Completeness (knowledge bases)
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A knowledge base KB is complete if there is no formular 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, you can make a consistent knowledge base 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 you have KB := { P(a), Q(a), Q(b) }, you have KB ⊭ P(b) and KB ⊭ ¬P(b), so with the closed world assumption you would get KB' = { P(a), ¬P(b), Q(a), Q(b) } where you have KB' ⊨ ¬P(b).
See also:
| v · d · eComputable knowledge |
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Topics and
concepts |
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Proposals and
implementations |
Zairja • Ars Magna ( Ramon Llull, 1300) • An Essay towards a Real Character and a Philosophical Language ( John Wilkins, 1688) • Calculus ratiocinator & Characteristica universalis ( Gottfried Leibniz, 1700) • Dewey Decimal Classification ( Melvil Dewey, 1876) • Begriffsschrift ( Gottlob Frege, 1879) • Mundaneum ( Paul Otlet & Henri La Fontaine, 1910) • Logical atomism ( Bertrand Russell, 1918) • Tractatus Logico-Philosophicus ( Ludwig Wittgenstein, 1921) • Hilbert's program ( David Hilbert, 1920s) • Incompleteness theorem ( Kurt Gödel, 1931) • Memex ( Vannevar Bush, 1945) • Prolog (1972) • Cyc (1984) • True Knowledge (True Knowledge Ltd., 2007) • Wolfram Alpha ( Wolfram Research, 2009) • Watson ( IBM, 2011) • Siri ( Apple, 2011)
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