Task 5

Question

Does a unifier exist for these pairs of predicates. If they do, give the unifier

i. Taller(x, John); Taller(Bob, y) ii. Taller(y, Mother(x)); Taller(Bob, Mother(Bob)) iii. Taller(Sam, Mary); Shorter(x, Sam) iv. Shorter(x, Bob); Shorter(y, z) v. Shorter(Bob, John); Shorter(x, Mary)

Answer

In logic and computer science, a unifier is a substitution that makes two or more predicates identical. Let's analyze each pair of predicates to determine if a unifier exists:

i. Taller(x, John); Taller(Bob, y)

Unifier:

After the substitution, both become Taller(Bob, John).

ii. Taller(y, Mother(x)); Taller(Bob, Mother(Bob))

Unifier:

After the substitution, both become Taller(Bob, Mother(Bob)).

iii. Taller(Sam, Mary); Shorter(x, Sam)

No unifier exists.

Reason: The predicates are not of the same type ('Taller' vs 'Shorter').

iv. Shorter(x, Bob); Shorter(y, z)

Unifier exists but is not specific.

Reason: Any values for x, y, z can be a unifier as long as x = y and z = Bob.

v. Shorter(Bob, John); Shorter(x, Mary)

No unifier exists.

Reason: The constants ('Bob', 'John', 'Mary') cannot be changed and there is no substitution that makes the predicates identical.