CSci 4511w: In Class Activities

Each week (except for the weeks when there is an exam) there will be an in-class activity. Activities will vary from discussion in small groups, to practical exercises and problem solving.
Participating will help you staying on top of the material and make sure you understand it. It will also help me understand what are the parts of the material you find most difficult.
Participation to each activity is worth 1% fo the class grade. If you miss class you cannot make up for the missing points, but there will be a few opportunities for extra credit during the semester.

Thursday January 21
This is part of question 2.2 from the textbook. We will examine the rationality of vacuum-cleaner agent functions given the following assumptions from the texbook:
- The performance measure gives one point for each clean square at each time step over a lifetime of 1000 steps.
- The environement is known a priori but the dirt distribution and initial location of the agent is not.
- The only actions available are Left, Right, Suck, No-op Left and Right move the agent left and right except when it will end up outside the environment, in which case it stays put.
- The agent perceives correctly its location and whether the location contains dirt.
1. You are given this reflex-vacuum-agent function:
```
function Reflex-Vacuum-Agent(location,status] returns an action
  if status = Dirty then return Suck
  else if location = A then return Right
  else if location = B then return Left
```
  Prove that this vacuum-agent function is rational. One way of doing it it to show that for all situationsm i.e. all distributions of dirt and all initial locations, there is no reflex-agent that can do better.
2. Suppose you change the performance measure so that one point is deducted for each movement. Should the agent function change? Does the agent need internal state?
Tuesday January 26
Reading of writing #1 and discussion in small groups.
Tuesday February 2
You are given the following graph, where each node has an identifier (a letter) and an h value. A number along an arc indicates the cost of the arc.
[figure to be added]
1. Show in what order A* expands nodes from Start to Goal. For each node expanded during the search show its f and g values. If a node is reached on multiple paths show its f and g values each time the node is reached, and indicate its parent node.
2. What is the solution path found?
Thursday February 11
Prove each of the following statements, or give a counterexample:
1. breadth-first search is a special case of A*
2. uniform-cost search is a special case of greedy best-first search
Tuesday February 16
Play a tic-tac-toe game with another student on a 4x4 board with the objective of placing 3 consecutive elements in a row/column/diagonal.
Write down the rules you use when deciding where to put your piece. Be as precise as possible, as if you were to describe an algorithm.
Tuesday February 23
Show the backed-up values for all the nodes in the following game tree and show the branches that are pruned by alpha-beta pruning. For each branch pruned, write down the condition that is used to do the pruning. Follow the convention used in the textbook to examine the branches in the tree from left to right. (Figure to be added)
Thursday March 11
[This is question 7.10 from the 3rd edition of rhe textbook and 7.8 from the 2nd edition] Decide whether each of the following sentences is valid, unsatisfiable, or neither. Verify your decisions using truth tables or equivalence rules.
1. Smoke → Smoke
2. Smoke → Fire
3. (Smoke → Fire) → (¬ Smoke → ¬ Fire)
4. Smoke ∨ Fire ∨ ¬ Fire
5. ((Smoke ∧ Heat) → Fire) ← ((Smoke → Fire) ∨ (Heat → Fire))
6. (Smoke → Fire) → ((Smoke ∧ Heat) → Fire)
7. Big ∨ Dumb ∨ (Big → Dumb)
8. (Big ∧ Dumb) ∨ ¬ Dumb
Thursday March 25
For each of the following sentences, decide if the logic sentence given is a correct translation of the English sentence or not. If not correct it and explain briefly why not.
1. No one owns a car
  ¬ (∀ x ¬ Own(x, y) ∧ Car(y))
2. One purple mushroom is poisonous.
  ∃ x Mushroom(x) ∧ Purple(x) ∧ Poisonous(x)
3. An object is clear if nothing is on it.
  ∃ x ∀ y Clear(x) → ¬ On(y,x)
4. John loves his dog.
  ∃ x Dog(x) ∧ Owns(John, x) → Loves(John, x)
5. John loves all his dogs.
  ∀ x Dog(x) ∧ Owns(John, x) ∧ Loves(John, x)
6. Every city has a dogcatcher who has been bitten by every dog in town.
  ∀ x ∀ y ∀ z City(z) ∧ DogCatcher(y) ∧ Dog(z) ∧ LivesIn(z,x) → BittenBy(y,z)
Thursday April 1
- write the statements and the negated goal in predicate calculus. Choose consistent predicates for the different sentences.
- translate the sentences to CNF
- Use resolution to show the knowledge base is contraddictory, hence the goal is proven.
Thursday April 8
- Consider the following sentences:
  1. At most one student knows the answer.
  2. One student knows the answer.
  3. Less than two students know the answer.
  4. At least one student knows the answer.
  5. Zero or one students know the answer.
  Circle the following sentence pairs that are logically equivalent:
  ab, ac, ad, bc, bd, be, cd, ce, de
- Translate each of the following sentences into first order logic:
  1. All pets are either cats or dogs.
  2. Nobody would harm a child.
  3. There are only two green boxes.
  4. The set of natural numbers is contained in the set of real numbers.
  5. Fido barks at raccoons.
Tuesday April 20
It is autumn, you need to rake leaves out of your yard. Assume that the yard is divided into a linear sequence of 5 squares each one meter on a side. The square at one end (S_0) is identified as the collection point. The goal is to get all the leaves into the collection point. Assume you have a leaf blower that can move all the leaves from square S_i to an adjacent square S_j. (inspired from a problem used by Drew McDermott).
- Write action schemas for the problem domain described above.
- Specify the initial state in which there are leaves in S_4, S_3, and S_1, and the leaf blower is in S_2.
- Specify the goal.
- Show the plan that a planner could construct to achieve the goal using the action schemas you defined.

Thursday April 29
Learn a decision tree using using information gain using the following data set (from Yoh-Han Pao, Adaptive Pattern Recognition and Neural Networks, 1980):

height	hair	eyes	class
tall	dark	blue	yes
short	dark	blue	yes
tall	blond	blue	no
tall	red	blue	no
tall	blond	brown	yes
short	blond	blue	no
short	blond	brown	yes
tall	dark	brown	yes

compute the entropy of the set S Entropy(S) = - p log₂ p - n log₂ n where p is the fraction of positive examples and n of negative examples
for each attribute A (i.e. for height, hair, and eyes)
1. split the examples into disjoint subsets, E_k for k=1,..d according to the value v of the attribute A. Each of those subsets corresponds to a branch in the decision tree from node A. For each subset compute its entropy:
  Entropy(S,A=v) = - p_k log₂ p_k - n_k log₂ n_k
  Entropy(S, height=tall) =
  Entropy(S, height=short) =
  Entropy(S, hair=dark) =
  Entropy(S, hair=blond) =
  Entropy(S, hair=red) =
  Entropy(S, eyes=blue) =
  Entropy(S, eyes=brown) =
2. after you have computed the entropy of each subset for each value of attribute A, compute the Gain, which is the expected reduction in entropy due to sorting on A, as follows:
  Gain(S,A) = Entropy(S) - sum{v in Values(A)} |S_v|/|S| Entropy(S_v)
  where S_v is the subset for which A has value v and Values(A) is the set of all possible values for A.
select the attribute that has the largest Gain and repeat the process until all subsets have have 0 entropy or you run out of attributes.

Thursday May 6
- Represent the following set of facts in a semantic net. ``Quakers are pacifists. Republicans are not pacifist. Nixon is a Quaker. Nixon is a republican.''
  If you want to find out if Nixon is a pacifist, what kind of difficulty will you encounter?
  What are possible methods for circumventing this difficulty?
- Represent the following sentence in predicate calculus and with a semantic network ``Paul cut down the tree with an axe''
- Suppose you decide to solve the missionaries and cannibals problem using planning. Write action schemas and show the initial and goal state.
- When you use backward search to do planning, why you do not add the negative literals that are in the effect of the action are not added to the state?