CS 607-A rt ifici al I nt ell ig ence Final Term Paper SEMESTER FALL 2005 www. vujannat.ning .com a) (5 marks) You are given the following statements: ZUYYXVVU→ ∧ → → ¬ ) .( 4 ) .( 3 . 2 . 1 Prove E usin g resolution refutation. Show all steps. ¬ b) (3+3+5 marks) The family tree below represents the relationships of a family: A B F C D G E H The dotted circles correspond to female family members, while the solid circles correspond to male family members. The arrows represent the parent-of relationship, e.g. A is a parent of F. You can see that A is the father of F while B is the mother of F. In a predicate logic representation of a family, we have the following predicate format: Spouse (Symbol a, Symbol b) Arguments: a is the spouse of b Mother (Symbol a, Symbol b): Arguments: a is the mother of b Gender (Symbol a, Symbol b: Female/Male): b is the gender of a
a) (5 marks) You are given the following statements:
Z U Y
Y X V
V
U
→∧
→→
¬
).(4
).(3
.2
.1
Prove E usin g resolution refutation. Show all steps. ¬
b) (3+3+5 marks) The family tree below represents the relationships of a family:
A B
F
CD
GE
H
The dotted circles correspond to female family members, while the solid circles correspond tomale family members. The arrows represent the parent-of relationship, e.g. A is a parent of F.You can see that A is the father of F while B is the mother of F.
In a predicate logic representation of a family, we have the following predicate format:Spouse (Symbol a, Symbol b) Arguments: a is the spouse of bMother (Symbol a, Symbol b): Arguments: a is the mother of bGender (Symbol a, Symbol b: Female/Male): b is the gender of a
(i) What constants would you define corresponding to the tree given?(ii) What predicates would you define for the above tree.
(iii) Give formulae using existential and universal quantifiers for the followingrelationships (You can use defined predicates in subsequent formulae, e.g. you canuse the predicate father in the defining the formula daughter). All the predicates taketwo arguments read as (arg1, arg2): arg1 is the <> of arg2a. Fatherb. Husbandc. Step-Fatherd. Maternal Aunt (Khaala)e. Maternal Grand Father (Naana)f. Grand Child, by song. Paternal Aunt (Phopho)
c) (3+3+3 Marks) Define the following terms. Give examples to support your definitions:
2. Operator:
3. Static Evaluation
Question2Waist is a fuzzy variable with universe of discourse 16 - 54 inches. The membership functions of Waist are Fat, Medium and Thin. Draw these membership functions on three separate graphs.
Q#3
Your problem is to generate a 32-bit word containing all 1's. Formulate the solution as a GA.
(i) Clearly write your GA steps.
(ii) Identify the initial population, fitness function, mutation andcrossover steps.
(iii) Can w e find the solution word w ith only using crossoveroperation? Support your answer w ith arguments?
Q#4
a) (5 marks) List and explain briefly the 5 steps of fuzzy inference.
b) (10 marks) Given the fuzzy system below, perform the inference graphically just like Matlabfor input A=0 and B=100. Briefly explain the steps you followed and how the output value of variable Y is obtained in no more than 10 sentences. Clearly state any assumption that you take inthe inference.
Consider the graph showing a road map for distances between cities. The values on the edges arethe distance between two adjacent cities. The values on the nodes are the under-estimates(heuristics) of the remaining distance. Construct a tree from the given graph and find the solutionusing the A* procedure considering A as the initial node, J as the destination node, and 12 as thebound value. Eliminate the bounded subtree(s) from your solutions and only show the resultanttree.
Q#1 Fuzzy system in the inherence method. 15 marks
Rule 1 Newspaper is simple, but does not cover all newspaper is below averageRule 2 Newspaper is harder to understand, but newspaper is averageRule 3 Newspaper is simple, And cover all newspaper average is above.Draw graph and write down steps.Note: Don’t use Matlab and just perform on exams software text area.
Q #2 15 marks1-Is a computer vision possible without AI techniques?2-Is here AI brain exists?3-Intelligence increases by age? Write comments .
Q#3 10 marksProve E by using of PONENS, TOLENS, INTRODUCTION, ELIMINATION Methods
(AvB) (C^-D)-E DAvB
Prove E by using Refutation Method.(A vE) (-D)
-E D
Q# 4 15 marksFind S and G and Candidate Elimination Method .
D A B C YES/NOD1 G I W 1D2 F I W 1D3 F J V 0D4 G K V 1D5 F K W 1
BEST SITE TO HELP STUDENTS (7+7 marks). Let us define the following propositions: A=x hates studying B=x wastes
time watching movies C=x attends VU lectures D=x gets a good grade in the AIcourse
i. Modus Ponens, Modus Tolens, AndElimination and AndIntroduction We know thatif a person hates studying, they waste time watching movies. We also know that if aperson does not hate studying and attends VU lectures, they will get a good grade in theAI course. There is a student who does not waste time watching movies and attends VUlectures, prove that this student will get a good grade in AI, using
ii. Resolution refutation. Also state, why do you think resolution refutation is a betterstrategy in practical theorem provers? (6 marks). Early man discovers fire in a
simplified chemistry world:
. • IF dry stones strike each other
. • Then a spark is produced
. • Conclusion
. • When there is a spark, dry leaves and oxygen is present in theatmosphere, then there is fire.. • Encode the problem using propositions and rules.. • One day, early man Fred rubbed dry stones together near a bunch of dryleaves (of coarse there was oxygen, or Fred would not be alive).
•Prove using resolution refutation that Fred created a fire. (5+5+5 marks). Discussthe three strategies of problem solving briefly. Give examples to support your argumentin each case.
i. Blind/UnInformed Searchesii. Informed/Heuristic Searchesiii. Optimal Searches (8+2 marks). Run the Alpha Beta Procedure on the following
tree clearly indicating the pruned branches. Calculate the percentage of nodes on whichthe static evaluation has to be computed.
Apply the Depth First Search on the tree given below to reach to the goal F(Highlighted)
Question No. 1 Marks : 10
**WARNING: Please note that Virtual University takes seriousnote of unfair means. Anyone found involved in cheating will getan `F` grade in this course.
c . Write all steps, missing steps may lead to deduction ofmarks.
b . If you believe that some essential piece of information ismissing, make an appropriate assumption and use it to solve
the problem.
a . If you think that there is something wrong with any of thequestions, attempt it to the best of your understanding.
2. Do not ask any questions about the contents of thisexamination from anyone.
1. Attempt all questions. Marks are written adjacent to eachquestion.
Please read the following instructions carefully beforeattempting any of the questions:
Time Allow ed: 90 Minutes Mid Term Examination – Spring 2006
Resolution refutation.i. Modus Ponens, Modus Tolens, And-Elimination and And-Introduction
We know that if a person hates cooking, he waste time watching movies. We alsoknow that if a person does not hate cooking and reads a lot of cook books, he willmake a great healthy meal everyday. Ali does not waste time watching movies andreads a lot of cook books, prove that Ali will make great healthy meals everyday,using
Y=x makes a great healthy meal everydayX=x reads a lot of cook booksV=x wastes time watching moviesU=x hates cooking
Suppose,
Question No. 3 Marks : 10
Describe how CNF (Conjunctive Normal Form) helps us in getting truth values of thelogical expressions in an efficient way.
Gives the short answer of the following:
Question No. 2 Marks : 5
Show all the steps you will perform using the table, showing the nodes in Open andVisited queue.
Show at least two iterations (or few if the solution is found in fewer than twoiterations). Clearly show your working for each step. Use both crossover andmutation. If you don’t get the desired result in two iterations, then output the [m c]pair that gives the best solution after two iterations.
[1 6] [2 7]
Find the parameters m and c for the line y = mx+c using a GA starting with the two
individuals in the initial population for [m c] as given below.
(x, y) : {(3,8) (7, 10)}
Given the two points in the x, y plane represented by (x, y) pairs as under
