Existential instantiation

Existential instantiation
Type	Rule of inference
Field	Predicate logic
Symbolic statement

In predicate logic, existential instantiation (also called existential elimination)^[1]^[2] is a rule of inference 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 $P\left({a}\right)$ , but its explicit statement is often left out of explanations.

In one formal notation, the rule may be denoted by

\exists xP\left({x}\right)\implies P\left({a}\right)

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

References

^ Hurley, Patrick. A Concise Introduction to Logic (11th ed.). Wadsworth Pub Co, 2008. Pg. 454. ISBN 978-0-8400-3417-5
^ Copi, Irving M.; Cohen, Carl (2002). Introduction to logic (11th ed.). Upper Saddle River, N.J.: Prentice Hall. ISBN 978-0-13-033737-5.

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[1] Hurley, Patrick. A Concise Introduction to Logic (11th ed.). Wadsworth Pub Co, 2008. Pg. 454. ISBN 978-0-8400-3417-5

[2] Copi, Irving M.; Cohen, Carl (2002). Introduction to logic (11th ed.). Upper Saddle River, N.J.: Prentice Hall. ISBN 978-0-13-033737-5.

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See also

References