Question

5. Prove the following Predicate Logic theorem using resolution refutation

• Premise 1. For all persons, a person’s mother is that person’s parent

2. For all persons, if the person’s parent is alive then the parent is older than the person

3. Mary is the mother of John

4. Mary is alive

• Conclusion?

1. Mary is older than John

Hint: use the following predicates

Mother(x,y): x is a mother of y

Parent(x,y): x is a parent of y

Older(x,y): x is older than y

Alive(x): x is alive

Answer 1

Using the given predicates, we can represent the given scenario in the following way:

• 
• 
• 
• 

We need to prove the following statement from these:

• 

We use the resolution refutation method to get the conclusion in the following way:

1. for all x and p [CNF of the first statement]
2. for all c and p [CNF of the second statement]
3. [third statement]
4. [fourth statement]
5. [negated conclusion]
6. [applying the resolution rule to 1 and 2]
7. [putting x=Mary and p=John in 6]
8. [applying the resolution rule to 4 and 7]
9. [applying resolution rule to 3 and 8]
10. [applying resolution rule to 5 and 9 we reach a contradiction]

Thus we arrive at a contradiction, and from the resolution refutation method, .

Hence, Mary is older than John.