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Theorem:
Herbrand (1930). If a sentence α is entailed by an FOL KB, it
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is entailed by a finite subset of the propositionalized KB
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Idea: For n
= 0 to ∞ do
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create a propositional KB by
instantiating with depth-n terms
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see if α is entailed by this KB
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Problem: works if
α is entailed, loops if α is not entailed
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Theorem: Turing
(1936), Church (1936) Entailment for FOL is
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semi-decidable (algorithms exist that say yes to every
entailed
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sentence, but no
algorithm exists that also says no to every non-
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entailed
sentence.)
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