Disjunction (Primitive Recursion)

Definition

Disjunction ( Primitive Recursion)

With representing false and representing true, disjunction is represented by the primitive-recursive function

Addition counts the true inputs; signum converts a positive count to . Thus

On Boolean inputs, the result is exactly when at least one input is . More generally, it returns exactly when at least one natural-number input is positive.

Construction

For Boolean inputs, the sum is , or . Returning the sum directly would give when both inputs are true. Signum maps both positive sums to the truth value :

Example

Converting the sum to a truth value