Talk:Existential instantiation

Not a Valid Rule
This is obviously not a valid rule: G |- exists x A(x) -- a not in G        G |- A(a) Its very easy to see, just take the rule for Universal generalization: G |- A(a) -- a not in G   G |- forall x A(x) So the existential instantion would basically also say that we can replace existential

quantifier by forall quantifier in the conclusion, which is of course not a sound inference.

Jan Burse (talk) 00:26, 17 February 2018 (UTC)


 * 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 as only replacing variables, while EI only adds new constant symbols (not variables). &mdash; Carl (CBM · talk) 03:59, 17 February 2018 (UTC)


 * 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. &mdash; Carl (CBM · talk) 04:02, 17 February 2018 (UTC)