Bai giai tri tue nhan tao tut 6

Trường Đại Học Bách Khoa Tp.Hồ Chí Minh

Khoa Khoa Học và Kỹ Thuật Máy Tính

Tutorial 6

PREDICATE LOGIC and

STRUCTURED KNOWLEDGE

Question 1:

Wrong in:

¬gt(5, 2) ∨ ¬succ(y, 2) combines with 6¬gt(x, y) ∨ ¬gt(y, z) ∨ gt(x, z) by the substitution

5/x, y/z

This combination is wrong because the variable y in each clause is different to each other.

To correct the resolution, we have to change the name of variable y in either first clause or

second clause.

Question 2:

What is wrong with the following argument:

• Men are widely distributed over the earth.

• Socrates is a man.

• Therefore, Socrates is widely distributed over the earth.

How should the facts represented by these sentences be represented in logic so that this

problem does not arise?

Solution

The conclusion is false because the property "widely distributed over the earth" is appli￾cable over a set (group of men). Not to each individual in the set.

To avoid that wrong conclusion, we can represent these facts like this:

man(Socrates).

widelyDistributed(men,earth)

Question 3:

Consider the following axioms:

1. All hounds howl at night.

2. Anyone who has any cats will not have any mice.

3. Light sleepers do not have anything which howls at night.

4. John has either a cat or a hound.

Use resolution with predicate logic to affirm the following conclusion:

If John is a light sleeper, then John does not have any mice.

Solution

Artificial Intelligence Exercises Page 1/5