# Practice examples on logic and resolution

• Transform into CNF (called also clause form) the following expression (taken from Winston):
```forall x [brick(x) implies
(therexist y [on(x,y) and not pyramid(y)]
and not therexist y [on(x,y) and on(y,x)]
and forall y [not brick(y) implies not equal(x,y)])]
```
• Translate the following sentences to predicate calculus:
1. John loves all his dogs.
2. Everyone who loves at least one of his cats is happy.
3. Not every student takes history and biology.
4. A mushroom is poisonous only if it is purple
5. No purple mushroom is poisonous
• Write in predicate calculus, and prove by resolution the following:
1. Anyone who can read is a literate. Dolphins are not literate. Some dolphins are intelligent. Prove: Some who are intelligent cannot read.
(from Luger & Stubblefield, Artificial Intelligence.)
2. If a course is easy, some students are happy. If a course has a final, no students are happy. Prove: If a course has a final, the course is not easy.
(from Luger & Stubblefield, Artificial Intelligence.)
3. Anyone passing his history exam and winning the lottery is happy. Anyone who studies or is lucky can pass all his exams. John did not study but he is lucky. Anyone who is lucky wins the lottery. Prove: is John happy?
(from Luger & Stubblefield, Artificial Intelligence.)
4. Sally studies with Morton. Morton is at the Union Building. Anyone who studies with someone who is at a place is also at that place. Anyone who is at a place is reachable at the telephone number of that place. Prove: what's the telephone number for Sally?
(from Luger & Stubblefield, Artificial Intelligence.)
5. Fido, the dog, goes wherever John, his master, goes. John is at the library. Prove: Where is Fido?
(from Luger & Stubblefield, Artificial Intelligence.)
6. Everyone has a parent. A parent of a parent is a grandparent. Prove: Who is the grandparent of John?"
(from Luger & Stubblefield, Artificial Intelligence.)
7. All people who are not poor and are smart are happy. Those people who read are not stupid. John can read and he is rich. Happy people have exciting lives. Prove: can anyone be found with an exciting life?
(from Luger & Stubblefield, Artificial Intelligence.)
8. Horses are faster than dogs. There is a greyhound that is faster than every rabbit. Harry is a horse. Ralph is a rabbit. Prove: Harry is faster than Ralph
(from Genesereth.)
9. A is on B, B on C. A is green,
C is blue. If something is green it is not blue.
Prove: there is a green block on a block that is not green."
10. All dogs howl at night.
Anyone who has any cats will not have any mice.
Light sleepers do not have anything which howls at night.
John has either a cat or a dog.
Prove: If John is a light sleeper, then John does not have any mice.
(This is long!)