Questions and Answers of Artificial Intelligence

Represent the sentence “All Germans speak the same languages” in predicate calculus. Use Speaks (x, 1), meaning that person x speaks language l.
What axiom is needed to infer the fact Female (Laura) given the facts Male (Jim) and Spouse (Jim, Laura)?
Write a general set of facts and axioms to represent the assertion ‘Wellington heard about Napoleon’s death” and to correctly answer the question ‘Did Napoleon hear about Wellington’s
Rewrite the propositional wumpus world facts from Section 7.5 into first-order logic. How much more compact is this version?
Write axioms describing the predicates Grand Child, Great Grandparent, Brother, Sister, Daughter, Son, Aunt, Uncle, Brother In Law, Sister In Law, and First cousin. Find out the proper definition of
Write down a sentence asserting that + is a commutative function. Does your sentence follow from the Peano axioms? If so explain why: if not, give a model in which the axioms are true and your
Explain what is wrong with the following proposed definition of the set membership predicate ???:
Using the set axioms as examples write axioms for the list domain, including all the constants, functions, and predicates mentioned in the chapter.
Explain what is wrong with the following proposed definition of adjacent squares in the wumpusworld:
Write out the axioms required for reasoning about the wumpus’s location, using a constant symbol Wumpus and a binary predicate In (Wumpus, Location). Remember that there is only one wumpus.
Extend the vocabulary from Section 8.4 to define addition for n-bit binary numbers. Then encode the description of the four-bit adder in Figure and pose the queries needed to verify that it is in
The circuit representation in the chapter is more detailed than necessary if we care only about Circuit functionality. A simpler formulation describes any rn-input, n-output gate or circuit using a
Prove from first principles that Universal Instantiation is sound and that Existential Instantiation produces an inferentially equivalent knowledge base.
From Likes (Jerry, Ice Cream) it seems reasonable to infer Эx Likes (x, Ice Cream). Write down a general inference rule, Existential Introduction that sanctions this inference. State carefully the
Suppose a knowledge base contains just one sentence Эx As High As (x, Everest). Which of the following arc legitimate results of applying Existential Instantiation?a. As High As (Everest,
For each pair of atomic sentences, give the most general unifier if it exists:a. P(A, B, B), P(x, y, z).b. Q(y, G (A, B)), Q (G(x, x), y)c. Older (Father (y), y), Older (Father(x), John).d. Knows
Consider the subscription lattices shown in Figure.a. Construct the lattice for the sentence Employs (Mother (John), Father (Richard)).b. Construct the lattice for the sentence Employs (IBM. y)
Suppose we put into a logical database a segment of the U.S. census data listing the age, city of residence, date of birth, and mother of every person, using social security numbers as identifying
One might suppose that we can avoid the problem of variable conflict in unification during backward chaining by standardizing apart all of the sentences in the knowledge base once and for all. Show
Explain how to write any given 3-SAT problem of arbitrary size using a single first-order definite clause and no more than 30 ground facts.
Write down logical representations for the following sentences, suitable for use with Generalized Modus Ponens:a. Horses, cows and pigs arc mammals.b. An offspring of a horse is a horse.c. Bluebeard
In this question we will use the sentences you wrote in Exercise 9.9 to answer a question using a backward-chaining algorithm.a. Draw the proof tree generated by an exhaustive backward-chaining
A popular children’s riddle is ‘Brothers and sisters have I none, but that man’s father my father’s son.” Use the rules of the family domain to show who that man is. You may apply any of
Trace the execution of the backward chaining algorithm in figure when it is applied solves the crime problem. Show the sequence of values taken on by the goals variable, and arrange them into a tree.
The following Prolog code defines a predicate P: P(X, [X | Y]). P (X, [Y| Z]):- P (X, Z).a. Show proof trees and solutions for the queries P (A, [1, 2, 3]) and P (2, [1, A, 3])b. What standard list
In this exercise, we will look at sorting in Prolog.a. Write Prolog clauses that define the predicate sorted (L), which is true if and only if list L is sorted in ascending order.b. Write a Prolog
In this exercise, we will look at the recursive application of rewrite rules, using logic programming. A rewrite rule (or demodulator in OTTER terminology) is an equation with specified direction.
In this exercise, we will consider the implementation of search algorithms in Prolog. Suppose that successor (X, Y) is true when state Y is a successor of state X; and that goal (X) is true when X is
How can resolution be used to show that a sentence is valid un-satisfiable?
From “Horses are animals:’ it follows that “The head of a horse is the head of animal.” Demonstrate that this inference is valid by carrying out the following steps:a. Translate the premise
Here are two sentences in the language of first-order logic:a. Assume that the variables range over all the natural numbers 0, 1, 2, . . , ∞ and that “>” predicate means “is
Resolution can produce non-constructive proofs for queries with variables, so we had to introduce special mechanisms to extract definite answers. Explain why this issue does not arise with knowledge
We said in this chapter that resolution cannot be used to generate all logical consequences of a set of sentences. Can any algorithm do this?
Write sentences to define the effects of the Shoot action in the wumpus world. Describe its effects on the wumpus and remember that shooting uses the agent’s arrow
Within situation calculus, write an axiom to associate time 0 with the situation S0 and another axiom to associate the time t with any situation that is derived from S0 by a sequence of t actions.
In this exercise, we will consider the problem of planning a route for a robot to take from one city to another. The basic action taken by the robot is Go (x, y), which takes it from City x to city y
Investigate ways to extend the event calculus to handle simultaneous events. Is it possible to avoid a combinatorial explosion of axioms?
Represent the following seven sentences using and extending the representations developed in the chapter:a. Water is a liquid between 0 and 100 degrees.b. Water boils at 100 degrees.c The water in
Write definitions for the following:a. Exhaustive Part Decompositionb. Part Partitionc. Part wise DisjointThese should he analogous to the definitions for Exhaustive Decomposition, Partition, and
Write a set of sentences that allows one to calculate the price of an individual tomato (or other object), given the price per pound. Extend the theory to allow the price of a bag of tomatoes to be
An alternative scheme for representing measures involves applying the units function to an abstract length object. In such a scheme, one would write Inches (Length (L1)) = 1.5. How does this scheme
Construct a representation for exchange rates between currencies that allows fluctuations on a daily basis.
This exercise concerns the relationships between event categories and the time intervals in which they occur,a. Define the predicate T(c, i) in terms of during and Є.b. Explain precisely why we do
Define the predicate Fixed, where Fixed (Location(x)) means that the location of object x is fixed over time.
Define the predicates Before, After, during, and Overlap, using the predicate Meet and the functions Start and End, hut not the function Time or the predicate <.
Section 10.5 used the predicates Link and Link Text to describe connections between web pages. Using the In Tag and Get Page predicates, among others, write definitions for Link and Link Text.
One part of the shopping process that was not covered in this chapter is checking for compatibility between items. For example, if a customer orders a computer, is it matched with the right
Add rules to extend the definition of the predicate Name (s, c.) so that a siring such as “laptop computer” matches against the appropriate category names from a variety of stores. Try to make
A complete solution to the problem of inexact matches to the buyer’s description in shopping is very difficult and requires a full array of natural language processing and information retrieval
Our description of Internet shopping omitted the all-important step of actually buying the product Provide a formal logical description of buying, using event calculus That is, define the sequence of
Describe the event of trading something for something else. Describe buying as a kind of trading in which one of the objects traded is a sum of money.
The two preceding exercises assume a fairly primitive notion of ownership. For example, the buyer starts by owning the dollar bills. This picture begins to break down when, for example, one’s money
You are to create a system for advising computer science undergraduates on what courses to take over an extended period in order to satisfy the program requirements. (Use whatever requirements are
Figure shows the top levels of a hierarchy for everything. Extend it to include as many real categories as possible. A good way to do this is to cover all the things in your everyday life. This
Recall that inheritance information in semantic networks can be captured logically by suitable implication sentences. In this exercise, we will consider the efficiency of using such sentences for
One might suppose that the syntactic distinction between unboxed links and singly boxed links in semantic networks is unnecessary, because singly boxed links are always attached to categories an
Describe the differences and similarities between problem solving and planning.
Given the axioms from Figure, what are all the applicable concrete instances of Fly (p, from, to) in the state described by At (P1, JFK) ^ At (P2, SF0) ^ Plane (P1) ^ Plane (P2) A Airport (JFK) ^
Let us consider how we might translate a set of STRIPS schemata into the successor-state axioms of situation calculus.• Consider the schema for Fly (p, from. to). Write a logical definition for the
The monkey-and-bananas problem is faced by a monkey in a laboratory with some bananas hanging out of reach from the ceiling. A box is available that will enable the monkey to reach the bananas if he
Explain why the process for generating predecessors in backward search does not need to add the literals that are negative effects of the action.
Explain why dropping negative effects from every action schema in a STRIPS problem results in a relaxed problem.
Examine the definition of bidirectional in,a. Would bidirectional state-space search be a good idea for planning?b. What about bidirectional search in the space of partial-order plans?c. Devise a
Prove the following assertions about planning graphs:a. A literal that does not appear in the final level of the graph cannot he achieved.b. The level cost of a literal in a serial graph is no
We contrasted forward and backward state-space search planners with partial-order planners, saying that the latter is a plan-space searcher. Explain how forward and backward state-space search can
Figure shows a blocks-world problem known as the Sussman anomaly. The problem was considered anomalous because the non interleaved planners of the early 1970s could not solve it. Write a definition
Consider the problem of putting on one’s shoes and socks, as defined in Section 11.3. Apply GRAPHPLAN to this problem and show the solution obtained. Now add actions for putting on a coat and a
The original STRIPS program was designed to control Shakey the robot Figure shows a version of Shakey’s world consisting of four rooms lined up along a corridor, where each room has a door and a
We saw that planning graphs can handle only propositional actions. What if we want to use planning graphs for a problem with variables in the goal, such as At (P1, x) ^ At (P2, x), where x ranges
Up to now we have assumed that actions arc only executed in the appropriate situations. Let us see what propositional successor-state axioms such as Equation (11.1) have to say about actions whose
Giving examples from the airport domain, explain how symbol-splitting reduces the size of the precondition axioms and the action exclusion axioms. Derive a general formula for the size of each axiom
In the SATPLAN algorithm in Figure, each call to the satisfiability algorithm asserts a goal g T where T ranges from 0 to Tmax. Suppose instead that the satisfiability algorithm is called only once,
Examine carefully the representation of time and resources in Section 12.1.a. Why is it a good idea to have Duration (d) be an effect of an action, rather than having a separate field in the action
A consumable resource is a resource that is (partially) used up by an action. For example, attaching engines to cars requires screws. The screws, once used, are not available for other
Give decompositions for the Hire Builder and Get Permit steps in Figure, and show how the decomposed sub plans connect into the overallplan.
Give an example in the house-building domain of two abstract sub plans that cannot be merged into a consistent plan without sharing steps.
Some people say an advantage of HTN planning is that it can solve problems like “take a round trip from Los Angeles to New York and back” that are hard to express in non-HTN notations because the
Show how a standard STRIPS action description can be rewritten as HTN decomposition, using the notation Achieve (p) to denote the activity of achieving the condition p.
Some of the operations in standard programming languages can be modeled as actions that change the state of the world. For example, the assignment operation copies the contents of a memory location,
Consider the following argument: In a framework that allows uncertain initial stares, disjunctive effects are just a notational convenience, not a source of additional representational power. For any
Why can’t conditional planning deal with unbounded indeterminacy?
In the blocks world we were forced to introduce two STRIPS actions, Move and Move to Table, in order to maintain the clear predicate properly. Show how conditional effects can be used to represent
Conditional effects were illustrated for the Suck action in the vacuum world—which square becomes clean depends on which square the robot is in. Can you think of a new set of propositional
Write out the full description of Suck for the double Murphy vacuum cleaner that sometimes deposits dirt when it moves to a clean destination square and sometimes deposits dirt if Suck is applied to
Find a suitably dirty carpet free of obstacles, and vacuum it. Draw the path taken by the vacuum cleaner as accurately as you can. Explain it, with reference to the forms of planning discussed in
The following quotes are from the backs of shampoo bottles. Identify each as an unconditional, conditional, or execution monitoring plan.(a) “Lather, Rinse, Repeat,’(b) “Apply shampoo to scalp
Specify in full the belief state update procedure for partially observable environments. That is, the method for computing the new belief state representation (as a list of knowledge propositions)
Write action descriptions, analogous to Equation (12.2), for the Right and Suck actions. Also write a description for Cheek Location, analogous to Equation (12.3). Repeat using the alternative set of
Look at the list of things that the re planning agent can’t do. Sketch an algorithm that can handle one or more of them.
Consider the following problem: A patient arrives at the doctor’s office with symptoms that could have been caused either by dehydration or by disease D (but not both). There are two possible
To the medication problem in the previous exercise, add a Jest action that has the conditional effect Culture Growth when Disease is true and in any case has the perceptual effect Know (Culture
Show from first principles that P (a│b ^ a) = 1.
Using the axioms of probability prove that any probability distribution on a discrete random variable must sum to 1.
Would it he rational for an agent to hold the three beliefs P (A) = 0.4, P (B) = 0.3, and P (A V B) = 0.5? If so, what range of probabilities would be rational for the agent to hold for A ^ B. Make
This question deals with the properties of atomic events, as discussed.a. Prove that (lie disjunction of all possible atomic events is logically equivalent to true.b. Prove that any proposition is
Consider the domain of dealing 5-card poker hands from a standard deck of 52 cards, under the assumption that the dealer is fair.a. How many atomic events are there in the joint probability
Given the full joint distribution shown in Figure, calculate the following: a. P (toothache) b. P (Cavity) c. P (Toothache ?cavity) d. P (Cavity ? toothache V catch).
Show that the three forms of independence in Equation (13.8) are equivalent.
After your yearly checkup, the doctor has bad news and good news. The bad news is that you tested positive for a serious disease and that the test is 99% accurate (i.e., the probability of testing
It is quite often useful to consider the effect of some specific propositions in the context of some general background evidence that remains fixed, rather than in the complete absence of

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