1:
(a) Give two examples of intelligent activity.
For each example explain briefly, why intelligence is required to perform that activity.
(6 marks)
(b) Define what is meant by the following.
i)
A predicate calculus expression S1 is satisfied.
ii)
A predicate calculus expression X logically follows from a set S of predicate
calculus expressions .
iii)
An inference rule is sound.
(6 marks)
(c) Represent the following as logical propositions.
If two sides of a triangle are equal, then the opposite angles are equal
Two sides of a triangle are not equal
(6 marks)
(d) If the propositions in part c) are assigned T prove using truth tables that it doesn’t
matter whether or not , The opposite angles are equal
(6 marks)
(e) Given the following set of Axioms all of which are assigned T
 [ a  b]  c
cd
de
eb
If  [ a  b] is T ,
prove  a is T, using Term Rewriting
(8 Marks)
(f)
Unify the following pairs of expressions if possible.
i) password( mary, favourite(Y,X)) with password(X, favourite(toy,f(X))
ii) p(a,b) with p(c,d)
iii) p(X,a,Y) with p(Z,Z,b)
iv) story(X, m(X), Y, Z) with story(baby_bear, Y1, d(X), goldilocks)
(8 Marks)
2:
“Research scientists in Artificial Intelligence try to get machines to exhibit behavior that
we call intelligent behavior when we observe it in human beings. “
(James R. Slagle (1971), Artificial Intelligence: The Heuristic Programming Approach
(New York: McGraw-Hill):
(a) Describe two behaviours which in your opinion, would be described as intelligent if
performed by a human but which wouldn’t be if carried out by a machine. In each case ,
give two reasons to support your choice.
(6 Marks)
(b) Define in your own words what is meant by Artificial Intelligence.
Outline three ways in which your definition improves on Slagles definition above.
(8 Marks)
(c) Describe briefly , three everyday applications which use Artificial Intelligence.
For each application say what functionality the Intelligent subsystem offers and how well
it performs in comparison to conventional systems.
(9 Marks)
(d) You have at your disposal the means to build the most intelligent computer system
ever to perform any task of your choosing. To which task would you apply this system to
and why?
Your answer should include a description of the task, and describe four benefits that an
intelligent system would bring to this task
(7 Marks)
3:
(a) Can the following expressions be unified?
f (X ,g ( f ( X, b), a, b)) with f ( g (a, Y, Z), Y).
X, Y , Z, are Variables
a,b are constants.
Give reasons for your answer.
(7 Marks)
(b) Write an algorithm to perform unification of two expressions in list form.
(8 Marks)
(c)Using the algorithm presented in part a), trace the unification of the following pairs
of expressions
f ( X, g( X, Y , h( Y ) ) ) and f ( g ( a, Y , Z), g ( U, b, Z) )
X, Y , Z, U are Variables
a,b are constants.
(15 marks)
4:
(a)
Using binary predicate symbols eq (=) and lt (<) and binary function symbols
sum (+) and prod (×), write down predicate calculus formulae that formalise
the following statements (some of which are false) about the natural numbers:
i)
There is a smallest number
ii)
There is no largest number
iii)
Every number is the sum of two squares
iv)
There exist two numbers whose product is less than their sum
(8 marks)
(b)
i) For the following formula describe an interpretation and variable assignment which
satisfies it.
(  X p(X))  (  X p(X))
ii ) For the formula below, state whether it is valid (true in all
interpretations) or not. Either give an informal justification of the validity, or
outline a falsifying interpretation.
(  X  Y p(X,Y))  (  Y  X p(X,Y))
(9 marks)
(c) Convert the following to clause form.
X [brick(X)  [ Y [ on(X,Y)  pyramid(Y)] 
Y [ on(X,Y)  on(Y,X)] 
Y [brick(Y)   eq(X,Y)]]]
If something is a brick, then it's on top of something which is not a pyramid, and nothing
is on it that it is also on, and it's not the same thing as anything other than a brick.
(13 marks)