From Russell and Norvig:

1. (15p) Exercises: 5p each
6.1, 6.2, 6.3

2. (7p) Model is a world in which sentence is true under particular
interpretation.  Consider a world in which there are only 4 propositions A,
B, C, D.  Suppose the following sentence in propositional logic

A ^ B

Since the sentence does not depend on C,D, we have four possible
models (corresponding to 4 different ways how to assign truth values to C
and D) of this sentence. How many models are there for following sentences ?

a)  A v B

b)  A ^ B ^ C
 

3. (10p)  7.2, 7.5

4. (15p) Consider the following propositional theory:

        (A)     ^
        (~A v D) ^
        (~A v ~D v C) ^
        (~B v ~C v D)
 

a) Is this theory in a normal form?  If so, which one?

b) Use resolution to prove:  C

c) Convert this theory into one with horn clauses, where the last in each
clause becomes the consequent of the horn clause.
 

5. (10p) Consider the kinship domain. The objects in this domain are
people, the properties they have include gender and they are related by
different relations such as parenthood, motherhood etc. Suppose we have
have two unary predicates Male and Female and binary predicates Child(x,y),
Sibling(x,y).

Write axioms describing predicates GrandChild, Brother, Sister,
Daughter, Son, Aunt and Uncle.  Use <=> to write the defintion of these
predicates (this is a smaller version of excercise 7.6)

6. (3p)  9.1
 

7. (10p) Write down the logical representation for th e
following sentences, suitable for use with Generalized Modus Ponens.

a)
1. Horses are mammals
2. An offspring of a horse is a horse.
3. Bluebeard is a horse.
4. Bluebeard is Charlie's parent.
5. Offspring and parent are inverse relations
(i.e. if x is an offspring of y then y is a parent of x
and if x is a parent of y then y is an offspring of x).
 

b) Using backward chaining proof that Charlie is a horse.