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Of course, a rule is not sound or complete on its own; the important question is whether a particular system of rules is together sound and compete. There are systems with EI that are sound and complete. But it can take a particular combination of other rules to achieve this. Normally, I think of UG
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Anyway, I've edited the article according to that understanding. It would be ideal for someone to look up a reference that has this rule, to see their entire system. — Carl
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quantifier by forall quantifier in the conclusion, which is of course not a sound inference.
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as only replacing variables, while EI only adds new constant symbols (not variables). — Carl
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So the existential instantion would basically also say that we can replace existential
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Its very easy to see, just take the rule for
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G |- exists x A(x) ------------------ a not in G G |- A(a)
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G |- A(a) ------------------ a not in G G |- forall x A(x)
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process or it was formerly listed at
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