In predicate logic, generalization (also universal generalization, universal introduction, GEN, UG) is a valid inference rule can be derived.

Generalization with hypotheses

The full generalization rule allows for hypotheses to the left of the turnstile.

. Without the second restriction, one could make the following deduction:

1. (Hypothesis)

2. (Existential instantiation)

3. (Existential instantiation)

4. (Faulty universal generalization)

is not being changed by the substitution of any variables).

Example of a proof

Prove:.

Proof:In this proof, universal generalization was used in step 8. The deduction theorem was applicable in steps 10 and 11 because the formulas being moved have no free variables.

See also

• First-order logic

• Hasty generalization

• Universal instantiation

• Existential generalization

References