| Proof of
completeness |
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| n | FC derives
every atomic sentence that is entailed |
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| by KB
(only for clauses in Horn form) |
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| 1. | FC reaches a fixed point (the deductive closure) |
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| where no new
atomic sentences are derived |
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| 2. | Consider the
final state as a model m, assigning |
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| true/false to
symbols |
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| 3. | Every clause in
the original KB is true in m |
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| a1 … ak
b |
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| 4. | Hence m
is a model of KB |
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| 5. | If KB╞
q, q is true in every model of KB, including m |
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