CS 4365 - Artificial Intelligence Test 2

[AI07-09] The algorithm described by Davis, Logemann, and Loveland (1962), so it is called DPLL takes as input a sentence in ____ - a set of clauses. Select the best answer.

CNF

(Entailment).(True ⊨ False) is ___.

False

[AI07-09] The following ____ rule is one of the seven inference rules for propositional logic. Select the best choice as discussed in the class.

Resolution

[Prolog] What would it be the result of T for the following prolog query??- [a, b, c] = [X, Y, Z | T].

T=[ ].

[AI-CSP] (AI-208) A variable in a CSP is ___ if every value in its domain satisfies the variable's binary constraints.

arc-consistent

[AI Ch14 BN2] As discussed in the class, one way to understanding the semantics of a Bayesian network is to view the Bayesian network as an encoding of a collection of ______ statements.

conditional independence

[Prolog] Write a prolog program (factorial/3 or factorial(N,A,F)) to compute a factorial F of an integer N, in tail-recursion with an accumulating variable A.

factorial(0,F,F).factorial(N,A,F) :- N > 0, A1 is N*A, N1 is N -1, factorial(N1,A1,F).

[AI07-09] With forward chaining, the final state of the inferred table reaches a(an) _____ where no new inferences are possible. The table contains true for each symbol inferred during the process, and false for all other symbols.

fixed point

[AI-CSP] Constraint satisfaction problems (CSP) on finite domains are typically solved using a form of search. What is not one of the most used techniques in CSP?

global search

[Prob] Logic is _______ in that adding new facts always expands a knowledge base.

monotonic

[AI-Ch10Plan] According to the authors. Consider Planning Graph. ____ links indicating literals that could not appeal together, regardless of the choice of actions.

mutex

(A ∨ B) ∧ (￢C ∨ ￢D ∨ E) ⊨ (A ∨ B) ∧ (￢D ∨ E) is ___.

unsatisfiable

[Prolog] Which of the following selections is correct?This ____ tests whether X is bound to a Prolog variable.

var/1

Select an equivalent statement for each statement below.

¬∃x p(x) = ∀x ¬p(x) ¬∀x p(x) = ∃x ¬p(x) ∃x p(x) = ∃y p(y) ∀x q(x) = ∀y q(y)

[Lecture13] According to the class discussion.New burglar alarm is installed at home. It is fairly reliable at detecting a burglary, but it also responds on occasion to minor earthquakes. There are 2 neighbors: John and Mary, who have promised to call you at work when they hear the alarm. What is P(¬B, ¬E, ¬A, ¬J, ¬M)?

(1-0.001)×(1-0.002) ×(1-0.001) ×(1-0.05) ×(1-0.01)

[Lecture13] According to the class discussion.Consider the following factoring equation and tables provided. [PICTURE MISSING] What is the answer for entry (1) in Table f(ExAxJxM) (that is, the right-most table)?

(E1) x (F1) + (E2) x (F2)

[Lecture13] According to the class discussion.Consider the following probability tables for fever (concerning only three causes of cold, flu, malaria). These causes are independent of each other and are all causes of Fever. What is the P(Fever |¬ Cold, ¬ Flu, Malaria) for the Entry (2)?

.9

[Prob] Given a sample space S which is not empty, the probability of an empty set is ________.

0

[Lecture13] According to the class discussion.Consider the following probability tables for fever (concerning only three causes of cold, flu, malaria). These causes are independent of each other and are all causes of Fever. What is the P(Fever | ¬ Cold, ¬ Flu, ¬ Malaria) for the Entry (1)?

0.0

[Lecture13] According to the class discussion.New burglar alarm is installed at home. It is fairly reliable at detecting a burglary, but it also responds on occasion to minor earthquakes. There are 2 neighbors: John and Mary, who have promised to call you at work when they hear the alarm. What is P( J ^ M ^ A ^ ¬B ^ ¬E)?

0.90 x 0.70 x 0.001 x 0.999 x 0.998

[Lecture12] According to the class discussion.Consider the wumpus world as shown below. The Known facts are: { not Pit[1,1], not Pit[1,2], not Pit[2,1] }, and the presence of breeze (denoted as b) in cells: b = { b[1,2], b[2,1] }. The Query is for the probability of Pit in each frontier cell of { [1,3], [2,2], [3,1] }, and especially to compute what is the probability of Pit in the cell [1,3], that is, P(Pit[1,3]). What is the normalization constant for this case to compute P(Pit13|known,b)? Select the best answer as discussed in the class.

1/((0.2)3 + 3x(0.2)2x0.8 + 0.2x(0.8)2)

Consider a vocabulary with only four propositions, A, B, C, and D. How many models are there for the following sentence? ¬A ∨ ¬B ∨ ¬C ∨ ¬D

15

[AI-Ch14BN] As discussed on Bayesian network (BN) in the class.If we assume n Boolean variables for simplicity with max k parents for each node (where k is much smaller than n), then the amount of information needed to specify each conditional probability table will be at most m numbers as a constant, and the complete network can be specified by n*m numbers (linear in n). In contrast, the joint distribution contains 2**n (2 to the power of n) numbers.To make this concrete, suppose we have n = 30 nodes, each with five parents (k=5). Then the Bayesian network requires ___ numbers, but the full joint distribution requires over a billion.

30*(2**5)

[Prolog] Which of the following selections is correct?This ____ tests whether X and Y are currently co-bound, i.e., have been bound to or share same value, or not, respectively.

==, \==

[Prolog] Consider the following op/3 predicate.?- op(500,yfx,'#').What is the result of the following query??- (A#B) = 1#2#3#4.

A = 1 # 2 # 3. B = 4.

[AI-Ch10Plan] According to the authors. Consider the blocks world and its theoretical complexity of planning and distinguish two decision problems. Consider the classical planning where the number of states is finite.Which one of the following statements is NOT correct?

Bounded PlanSAT problem is semidecidable for classical planning.

[AI-Ch14BN] As discussed on Bayesian network (BN) in the class.In a polytree network, one would need to issue O(n) queries costing O(n) each, for a total of O(n*n) time. Consider clustering algorithms. Which one of the following choices is NOT correct?

Clustering algorithms are not widely used in commercial systems for its overhead.

[AI-Ch10Plan] According to the authors. Consider mutex condition in a planning graph. One of the preconditions of one action is mutually exclusive with a precondition of the other. This describes _____.

Competing needs

[AI-CSP] (AI-212) For example, in an airline-scheduling problem in CSP, let's suppose there are two flights, F1 and F2, for which the planes have capacities 165 and 385, respectively. The initial domains for numbers of passengers on each flight are then D1 = [0, 165] for F1, and D2 = [0,385] for F2. Now suppose we have the additional constraint that two flights together must carry 420 people (F1 + F2 = 420). We reduce the domains to ____

D1=[35,165] and D2=[255,385]

The following step in conversion from (1) FOL to (2) Clausal form is to ___. [1] ∀x [∀y Animal(y) ⇒ Loves(x, y)] ⇒ [∃y Loves(y, x)] [2] ∀x [¬ ∀y ¬ Animal(y) ∨ Loves(x, y)] ∨ [∃y Loves(y, x)]

Eliminate Implications

(Entailment - True/False)Note: a ⊨ b. This reads "a entails b". M(X) is a model of X.a ⊨ b if M(a) contains M(b).

False

If α ⊨ (β ∨ γ) then α ⊨ β or α ⊨ γ

False

[AI07] ____, who developed full first-order logic in 1879, based his system of inference on a collection of valid schemas plus a single inference rule, Modus Ponens.

Gottlob Frege

[AI07-09] Deciding entailment with ____ clauses can be done in time that is linear in the size of the knowledge base.

Horn

[Prolog] Explain the behavior or goal of the following program xyz/3.xyz(X,[X|R],R).xyz(X,[F|R],[F|S]) :- xyz(X,R,S).?- xyz(X,[1,2,3],L).

It will take an element X out of a list [X|R], resulting in a list R.

The frame problem was first recognized by ____ and Hayes. Many researchers considered the problem unsolvable within first-order logic, and it spurred a great deal of research into nonmonotonic logics. The solution of the frame problem with successor-state axioms is due to Ray Reiter (1991). Thielscher (1999) identifies the inferential frame problem as a separate idea and provides a solution.

John McCarthy

[AI07] Logical state estimation, of course, requires a logical representation of the effects of actions—a key problem in AI since the late 1950s. The dominant proposal has been the situation calculus formalism by _____ (1963), which is couched within first-order logic.

John McCarthy

[AI07-09] Consider logical systems which are monotonic. For any sentences α and β, if KB |= α then ____.

KB ∧ β |= α

[AI07] ___ showed that a complete procedure for inference in first-order logic could be obtained via a reduction to propositional logic,using Herbrand's theorem (Herbrand, 1930).

Kurt Gödel

[Prolog] What is the result of the following query??- parent(a,X) = .. L.

L = [parent, a, _X001]

[AI-Ch10Plan] According to the authors. Consider Planning Graph. The graph and the no-goods will always level off. The key to this proof is that certain properties of planning graphs arc monotonically increasing or decreasing. "X increases monotonically" means that the set of Xs at level (i+1) is a superset (not necessarily proper) of the set at level i.Which one of the following choices is NOT correct?

Level cost of Goal decrease monotonically

[AI Ch14 BN2] As discussed in the class, consider the following definition of Markov blanket and the figure shown below. Which one of the following choices is NOT in the Markov blanket of the node I? The Markov blanket of a variable A is the set consisting of the parents of A, the children of A, and the variables sharing a child with A.

M

The following ____ rule is one of the seven inference rules for propositional logic. Select the best choice as discussed in the class.

Modus Ponens

[AI Ch14 BN2] As discussed in the class, using chain-rule over the joint probability distribution over X={a, b, c}, then P(a, b, c) = _____.

P(a | bc) P(b | c) P(c)

[Lecture12] According to the class discussion.Consider the axioms of Probability (where a and b are random variables). Which one of the following is NOT correct?

P(a ∧ b) = P(a) * P(b)

The following step in conversion from (1) FOL to (2) Clausal form is to ___. [1] ∀x [∃ y Animal(y) ∧ ¬ Loves(x, y)] ∨ [∃z Loves(z, x)] [2] ∀x [Animal(F(x)) ∧ ¬ Loves(x, F(x))] ∨ Loves(G(x), x)

Skolemize

[AI-Ch10Plan] According to the authors. Consider Planning Graph. Which one of the following choices is NOT correct?

The consistency of an action at one level assures the preconditions and effects at one level to the next.

(Entailment)(C ∨ (￢A ∧ ￢B)) ≡ ((A ⇒ C) ∧ (B ⇒ C)) is ___.

True

(Entailment)α ≡ β if and only if the sentence (α ⇔ β) is valid.

True

(Entailment)α ⊨ β if and only if the sentence (α ∧ ￢β) is unsatisfiable.

True

Entailment. (A ∨ B) ∧ (￢C ∨ ￢D ∨ E) ⊨ (A ∨ B) is ___.

True

[AI07-09] This is ____ that the sentence x = 0 entails the sentence xy = 0.

True

[Lecture12] According to the class discussion. Consider a Medical diagnosis for Meningitis which is a disease caused by the inflammation of the protective membranes covering the brain and spinal cord known as the meninges. A doctor knows that meningitis causes a stiff neck 50% of the time: P(s|m)=0.5. The doctor also knows some unconditional facts: the prior probability that the patient has meningitis is 1/50000. That is, P(m)=1/50000. The prior probability that any patient has a stiff neck is 1/20. That is, P(s)=1/20. What is P(m | s)?

[ 0.5 x (1/50000) ] / (1/20)

[AI-Ch10Plan] According to the authors. Consider Planning Graph. To estimate the cost of a conjunction of goals, there are three simple approaches. This ____ heuristic is admissible and it dominates the other heuristics, and it works extremely well on tasks in which there is a good deal of interaction among subplans. It is not perfect, of course; for example, it ignores interactions among three or more literals.

[AI-Ch10Plan] According to the authors. Consider Planning Graph. Planning is ______.

[AI-Ch10Plan] According to the authors. Consider Planning Graph. An estimate using the level cost of each goal literal might not always be accurate, however, because planning graphs allow several actions at each level, whereas the heuristic counts just the level and not the number of actions. Further the estimates using these level costs are _____ for the individual goals.

admissible

[AI-CSP] (AI-212) The Alldiff constraint in CSP says that all the variables (Vars) involved must have distinct values (as discussed in the book and class). In SWI-Prolog CLP, it is done via ___ for variables Vars.

all_different(Vars)

[AI-Ch10Plan] According to the authors. One issue in planning is deciding which actions are candidates to regress over. In the forward direction we chose actions that were (1) _____ —those actions that could be the next step in the plan. In backward search we want actions that are (2) _____ —those actions that could be the step in a plan leading up to the current goal state.

applicable, relevant

[Prob] Beliefs ____________.

are changeable

This ____ is to add a new fact or rule (clause).

assert/1

[Prolog] Which of the following selections is correct?This ____ tests whether X is bound to a symbolic atom.

atom/1

[Lecture12] According to the class discussion, a(n) ____ event is a complete specification of the state of the world about which the agent is uncertain. If the world is described by a set of random variables, a(n) _____ event is a particular assignment of values to the random variables.

atomic

The first complete algorithm of _____ is often called the Davis-Putnam algorithm, after the seminal paper by Martin Davis and Hilary Putnam (1960). The algorithm is in fact the version described by Davis, Logemann, and Loveland (1962), so it is called DPLL after the initials of all four authors.

backward chaining

[AI07-09] _____ is a form of goal-directed reasoning. Select the best answer.

backward chaining

[Prob] Partial-information games are solved using ___________.

belief states;

[Prob] Truth maintenance may alter ________.

beliefs

[AI-CSP] (AI-212) A CSP is ___ if for every variable X, and for both the lower-bound and upper-bound values of X, there exists some value of Y that satisfies the constraint between X and Y for every variable Y.

bounds consistent

This ____(P) forces P to be a goal; succeed if P does, else fail.

call/1

[Lecture13] According to the class discussion.New burglar alarm is installed at home. It is fairly reliable at detecting a burglary, but it also responds on occasion to minor earthquakes. There are 2 neighbors: John and Mary, who have promised to call you at work when they hear the alarm. Each probability table (for each node) is _____. Select the best answer.

conditional

As discussed in the class, consider the example of the joint probability distribution of (Toothache, Catch, Cavity) as shown below. Here Cavity separates Toothache and Catch because it is a cause to both of them with a naïve assumption: "Toothache and Catch" are [or believed to be] _____.

conditionally independent

[Lecture12] According to the class discussion. The following formula is an example of ____ rule. Given two random variables Y and Z, P(Y) = Σ P(Y|Z) P(Z)

conditioning rule

[AI-CSP] (AI-216) This ___ heuristic attempts to reduce the branching factor on future choices by selecting the variable that is involved in the largest number of constraints on other unassigned variables.

degree

[AI07-09] The DPLL algorithm generates essentially a ____ enumeration of possible models.

depth-first

[Prob] Bayesian reasoning is ___________

diagnostic

[AI07-09] An alternative definition of equivalence is as follows: any two sentences α and β are equivalent only if each of them ___ the other

entails

[AI-CSP] A constraint involving an arbitrary number of variable is called ___.

global constraint

[Prob] Any probability value is ____________

in the range of 0 to 1

[Prolog] What is the following mystery/2 about (using member/2)?mystery([X|Y],M,[X|Z]) :- member(X,M), mystery(Y,M,Z).mystery([X|Y],M,Z) :- \+ member(X,M), mystery(Y,M,Z).mystery([],M,[]).

intersection

[AI-Ch10Plan] According to the authors. The reason for the state, "not Poor," is NOT allowed in PDDL because _____.

it is negated

[AI-Ch10Plan] According to the authors. With a planning graph, one can estimate the cost of achieving any goal literal G from a state S as the level at which the goal literal G first appears in planning graph constructed from initial state S. We call this the ______ of G.

level cost

[AI-Ch10Plan] According to the authors. Consider Planning Graph. To estimate the cost of a conjunction of goals, there are three simple approaches. The ____ heuristic, following the subgoal independence assumption, returns the sum of the level costs of the goals.

level-sum

[AI-Ch14BN] As discussed on Bayesian network (BN) in the class.If the number of parents of each node of a polytree network is bounded by a constant, then the complexity will also be ______ in the number of nodes.

linear

[AI-Ch14BN] As discussed on Bayesian network (BN) in the class.The time and space complexity of exact inference in polytree is ____ in the size of the network where the size is defined as the number of CPT entries.Select the best answer.

linear

[AI-Ch10Plan] According to the authors. Consider Planning Graph. To estimate the cost of a conjunction of goals, there are three simple approaches. The _____ heuristic simply takes the maximum level cost of any of the goals. This heuristic is admissible, but not necessarily accurate.

max-level

[Prolog] Write a prolog program for member/2 where member(X, Y) checks whether X is an element of a list Y.

member(X,[X|R]).member(X,[Y|R]) :- member(X,R).

[AI-Ch10Plan] According to the authors. One can reduce the branching factor without ruling out any solutions by always using the action formed by substituting the ______ into the (standardized) action schema.

most general unifier

[AI-Ch10Plan] According to the authors. Consider Planning Graph. As a tool for generating accurate heuristics, we can view Planning Graph as a relaxed problem that is efficiently solvable. To understand the nature of the relaxed problem, we need to understand exactly what it means for a literal G to appear at level Si in the planning graph. Ideally, we would like it to have a guarantee that there exists a plan with i action-levels that achieves g, and also that if the literal G does not appear, there is no such plan. Unfortunately, making that guarantee is as difficult as solving the original planning problem. So Planning Graph makes the second half of the guarantee (if the literal G does not appear, there is no plan), but if the literal G does appear, then all Planning Graph promises is that there is a plan that possibly achieves the literal G and has no "obvious" flaws. An obvious flaw is defined as a flaw that be detected by considering two actions or two literals at a time—in other words, by looking at the _____ relations.

mutex

[AI-Ch10Plan] According to the authors. For an action to be relevant to a goal it obviously must contribute to the goal: at least one of the action's effects (either positive or negative) must unify with an element of the goal. What is less obvious is that the action must not have any effect (positive or negative) that ____ an element of the goal.

negates

[Prob] If one can add new fact to knowledge base or delete it from a knowledge base, this is an example of ________reasoning.

nonmonotonic

[AI-Ch10Plan] According to the authors. Consider Situation Calculus. Each action's preconditions arc described with a(n) _____ axiom that says when the action can be taken.

possibility

[Prolog-4] As discussed in the class. Select the correct definition of prefix/2 (assuming append/3 provided).

prefix(P, L) :- append(P, _, L).

[Prob] Probabilities of different event outcomes are a(n) ___________

probability distribution

[AI-Ch10Plan] According to the authors. In regression search we start at the goal and apply the actions backward until we find a sequence of steps that reaches the initial state. It is called _____-states search because we only consider actions that are closely related or applicable to the goal (or current state).

relevant

The question of entailment for first-order logic is _____. That is, algorithms exist that say yes to every entailed sentence, but no algorithm exists that also says no to every nonentailed sentence.

semidecidable

[AI-Ch14BN] As discussed on Bayesian network (BN) in the class.With this family of ____ networks, there is at most one undirected path between any two nodes in the network.

singly-connected

[Prolog] Using append/3, what would be the definition for suffix of a list?

suffix(S,L) :- append(_,S,L).

[AI-Ch10Plan] According to the authors. The book introduces a language called PDDL (the Planning Domain Definition Language) that allows us to express all 4Tn 2 actions with one action schema (for Wumpus world of n*n grid for time T, probing 4 sides of each cell at a time). PDDL describes the four things we need to define a search problem: _____. Which one of the following choices is NOT correct?

the plan domain

[AI-Ch10Plan] According to the authors. A planning graph, once constructed, is a rich source of information about the problem. If any goal literal fails to appear in the final level of the graph, then the problem is _____.

unsolvable

There are two discrete random variables X and Y where X describes weather conditions, with the domain: X={sunny, rain, cloudy, snow}, and Y describes clothes to wear, with the domain: Y={t-shirt, long-sleeves, coat}. The distributions of X and Y are: X = <0.331, 0.26, 0.159, 0.25> Y = <0.5, 0.3, 0.2> And the joint probabilities are: P(t-shirt, sunny)=0.32 P(t-shirt, rain)=0.08 P(t-shirt, cloudy)=0.09 P(t-shirt, snow)=0.01 P(long-sleeves, sunny)=0.01 P(long-sleeves, rain)=0.15 P(long-sleeves, cloudy)=0.05 P(long-sleeves, snow)=0.09 P(coat, sunny)=0.001 P(coat, rain)=0.03 P(coat, cloudy)=0.019 P(coat, snow)=0.15

α (0.32+0.08+0.09+0.01) = 1

What is the predicate form of the following statement? "No drug pusher was a VIP"

∀x [d_pusher(x) ⇒ ¬ VIP(x)]

What is the predicate form of the following statement? "Some of the drug pushers entered this country and they were only searched by drug pushers"

∃x ∀y [entered_country(x) ∧ d_pusher(x)] ∧ [searched(y,x) ⇒ d_pusher(y)]