predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifi ...

, existential instantiation (also called existential elimination)Moore and Parker is a

rule of inference In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of in ...

which says that, given a formula of the form

(\exists x) \phi(x)

, one may infer

\phi(c)

for a new constant symbol ''c''. The rule has the restrictions that the constant ''c'' introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. It is also necessary that every instance of

x

which is bound to

\exists x

must be uniformly replaced by ''c''. This is implied by the notation

P\left(\right)

, but its explicit statement is often left out of explanations. In one formal notation, the rule may be denoted by :

\exists x P \left(\right) \implies P \left(\right)

where ''a'' is a new constant symbol that has not appeared in the proof.

References

Rules of inference Predicate logic {{logic-stub

See also

References