CIS603 S03: Homework 3

1. Resolution Theorem Proving

Consider the following information:

1. Animals can outrun any animals that they can eat.
2. Carnivores eat other animals.
3. Outrunning is transitive: if x can outrun y and y can outrun z, then x can outrun z.
4. Lions eat zebras.
5. Zebras can outrun dogs.
6. Dogs are carnivores.

2. First order logic

Represent the following sentences in first-order logic using a consistent vocabulary (which you must define):

1. Not all students take both History and Biology.
2. Only one student failed History.
3. Only one student failed both History and Biology.
4. The best score in History was better than the best score in Biology.
5. Every person who dislikes all vegeterians is smart.
6. No person likes a smart vegeterian.
7. There is a woman who likes all men who are vegeterians.
8. There is a barber who shaves all men in town who do not shave themselves.
9. No person likes a professor unless the professor is smart.
10. Politicians can fool some of the people all of the time, and they can fool all of the people some of the time, but they can't fool all of the people all of the time.

3. Problem 9.4 from the textbook, pg 316

4. Unification

What is the most general unifier for the expressions, where letters early in the alphabet are object constants, and letters late in the alphabet are variables.

p= f(x1, g(x2, x3), x2, b) and q = f(g(h(a, x5), x2), x1, h(a, x4), x4)

p = j(f(x, g(x,y)), h(z,y)) and q = j(z, h(f(u,v), f(a,b)))

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