意大利罗马第一大学2012年2月15日Artificial Intelligence人工智能考试题及答案(英)

Arti?cial Intelligence I

Luigia Carlucci Aiello

February15,2012

First Name and Last name ..................................................................................................................................................

I do allow the results of this examination to be posted online,on the course web site.

YES[]NO[]

Signature ................................................................................................................................................

You have2hours and30minutes.You can use neither the text books nor your notes.

To pass the exam,it is necessary to answer su?ciently all the sections.

Answer the questions of section G1directly on this page,which will be taken at identity-check time.

?G1.(4points)

?(1/2point)

In a dynamic environment changes occur not necessarily because of agent actions.

Solution:

TRUE:It is the de?nition.

?(1/2point)

The algorithm A?always?nds an optimal solution.

Solution:

FALSE:A??nds an optimal solution if the heuristic function is admissible.

?(1/2point)

P(b+a,a,b+y)and P(x,a,b+a)(where a and b are constants and x and y are variables) unify.

Solution:

TRUE:with{ x/b+a , y/a }

?(1/2point)

The negation of a satis?able formula is always satis?able.

Solution:

FALSE:It could be a contradiction.

?(1/2point)

It is possible to build a knowledge based agent that is a pure re?ex agent.

Solution:

TRUE:Although the KB is a memory,the agent could use it just to hold re?ex rules.

?(1/2punto)

The propositional formula(P∧?R)→(Q→R)can be converted into a Horn clause. Solution:

TRUE:?P∨?Q∨R or(P∧Q)→R.

?(1/2point)

In Prolog,in the list[A|B],B represents the last element of the list.

Solution:

FALSE:A is the head of the list,while B is the tail.

?(1/2point)

In Prolog,the best way to represent the brotherhood relationship between Vittorio and Enrico is through the list[vittorio,enrico].

Solution:

FALSE:A list represents a collection,not a relationship.Indeed the best way to represent the relationship is through a predicate like brother(vittorio,enrico).

?G2.(8points)Prolog(5credits)

–Exercise2.1(3points)(5credits)

Explain what the following program foo/3does.The solution must contain an adequate explanation and an example.Assume queries like foo([1,4,5],[2,3,6],X).

foo([],[],[]).

foo([A|R1],[B|R2],[A,B|R]):?A

foo([A|R1],[B|R2],R):?A>=B,foo(R1,R2,R).

Solution:

The program,if given two lists of numbers of the same size,returns a new list that is a combination of the two.In particular,it scans the two lists pairwise(i.e.,the?rst element of the?rst list and the ?rst element of the second,then the second element of the?rst list and the second element of the second one,etc...)and if the element of the?rst list is smaller than the one in the second one,it adds both to the result.It skips them otherwise.In the example query,foo returns X=[1,2,5,6].

–Exercise2.2(5points)(5credits)

Suppose we are given a knowledge base with the following facts:

tran(uno,one).

tran(due,two).

tran(tre,three).

tran(quattro,four).

tran(cinque,five).

tran(sei,six).

tran(sette,seven).

tran(otto,eight).

tran(dieci,nine).

Write a predicate listtran(G,E)which translates a list of Italian numerals into the cor-responding list of English ones.For example:listtran([uno,nove,due],X).should return: X=[one,nine,two].

The program should also work in the other direction.For example,if you give it the query listtran(X,[one,seven,six,two]).it should return:X=[uno,sette,sei,due].

Solution:

listtran([],[]).

listtran([A|Rest1],[B|Rest2]):?tran(A,B),listtran(Rest1,Rest2).

listtran([A|Rest1],[B|Rest2]):?tran(B,A),listtran(Rest1,Rest2).

?G2’.(8points)Prolog(6credits)

–Exercise2.1’(3points)

Explain what the following program foo/1does.Moreover,describe what the predicates ioo and bar represent.The solution must contain an adequate explanation and an example.

ioo(bar(4,bar(6,void,void),bar(1,bar(8,void,void),void))).

foo(S):?ioo(I),foo(I,S).

foo(void,0).

foo(bar(C,A,B),S):?C<7,!,foo(A,S1),foo(B,S2),S is S1+S2+1.

foo(bar(,A,B),S):?foo(A,S1),foo(B,S2),S is S1+S2.

Solution:

ioo is a predicate that de?nes the input,while bar represents a binary tree.Given a binary tree I de?ned by the predicate ioo,the procedure returns the number of elements in I that are smaller than7.The cut is a red cut as removing it changes the meaning of the program.In the example, the procedure returns3.

–Exercise2.2’(5points)

Given a graph G and a source node N,verify that G is a direct acyclic graph(DAG).Assume that:

1.G is already available in the knowledge base;

2.All nodes are reachable from N;

3.Every node has exactly two outgoing edges or has none;

4.Each edge has a label denoting if it is the?rst or second outgoing edge of a node.

The following example represents a DAG as described above:

edge(a,b,1).

edge(a,c,2).

edge(b,c,1).

edge(b,e,2).

edge(c,d,1).

edge(c,e,2).

Important:The program must:

https://www.360docs.net/doc/a318221634.html,e the fail-cut combination to fail when encountering a loop;

https://www.360docs.net/doc/a318221634.html,e a red cut;

3.not be longer than4rules.

Solution:

isdag(N1):?isdag(N1,[N1]).

isdag(N1,V isited):?edge(N1,N2,),member(N2,V isited),!,fail.

isdag(N1,V isited):?edge(N1,N2,1),edge(N1,N3,2),!,

isdag(N2,[N2|V isited]),isdag(N3,[N3|V isited]).

isdag(,).

?G3.(14points)Agents and Search

–Exercise3.1(4points)

Illustrate the de?nition and the main properties of heuristic functions.Illustrate and compare at least two di?erent heuristic functions for the Eight Puzzle.

Solution:

Please refer to the textbook for de?nition and properties.

Heuristic functions for the eight puzzle:

1)Number of misplaced tiles

2)Manhattan distance

Both admissible,the second one is better as it dominates over the?rst one.

–Exercise3.2(10points)

Consider the following game:there are three black tiles B,three white tiles W,and an empty space?in this initial con?guration:

B|B|B|W|W|W|?|

The game consists in moving a tile:

1)to an adjacent position if it is empty;

2)jumping over one or two tiles to land in the empty space.

The cost of moving a tile to an adjacent position is one;the cost of a jump is1plus the length of the jump(i.e.,2or3).

The goal of the game is moving all the black tiles to the right of all the white ones;we do not care about the position of the empty space.A possible goal state is:

W|W|W|?|B|B|B|

Specify an admissible heuristic function and draw the tree generated by A?using the chosen heuristics.

Solution:

The operator

Moveright(i,j)

Preconditions:

1≤i,j≤7

i

either i or j is?

j?i≤3

E?ect:

The content of i and j are exchanged.

Cost:

j?i

Examples of(admissible)heuristic functions h(n)are the following ones

1)the number of black tiles still sitting at the left of at least one white tile

2)the number of black tiles still sitting at the left of the leftmost white tile plus the number of white tiles still sitting at the right of the rightmost black tile

3)the number of black tiles at the left of each white one.

Once the heuristic is chosen,the expansion of A?is routine.

?G4.(12points)Logic and Knowledge Representation

–Exercise4.1(6points)

Let

Rectangle(r)be“r is a rectangle”;

Square(q)be“r is a square”;

Side(s,r)be“s is a side of r”;

P arallel(s1,s2)be“the sides s1and s2are parallel”;

Right(s1,s2)be“the angle in between s1and s2is right”;

len(s)be the function that gives the length of s.

Represent as?rst order formulas the following sentences.

1.A rectangle has four sides,two pairs of parallel sides,and four right angles.

2.A square is a rectangle whose sides have the same length.

Solution:

1.?r Rectangle(r)??[?s1?s2?s3?s4(s1=s2)∧(s2=s3)∧(s3=s4)∧(s4=s1)∧

Side(s1,r)∧Side(s2,r)∧Side(s3,r)∧Side(s4,r)∧P arallel(s1,s2)∧P arallel(s3,s4)∧Right(s1,s2)∧Right(s2,s3)∧Right(s3,s4)∧Right(s4,s1)]

2.?r Square(r)??[Rectangle(r)∧(?s1?s2(Side(s1,r)∧Side(s2,r))→len(s1)=len(s2))]

–Exercise4.2(6points)

Represent as propositional formulas the following sentences:

1.If it rains,the lawn is wet.

2.If the sprinkler is on,the lawn is wet.

3.If the gardner passed by,the sprinkler is on.

a)We observe that the lawn is wet.Is this observation consistent with the fact that it rains

and that the gardner passed by?

b)The gardner passed by.Can we infer that the lawn is wet?

In both cases use the tableaux.

Solution:

Part a)

1.R→W

2.S→W

3.G→S

Case a)

4.W

We expand a tableau for the above formulas and

5.R∧G

The tableaux is complete and open,hence5is consistent with1–4. Case b)

4 .G

We expand a tableau for the above formulas and

5 .?W

The tableaux closes,hence W can be derived from1–3,4’and5’.