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Artificial Intelligence Foundations Of Computational Agents 2nd Edition David L. Poole, Alan K. Mackworth - Solutions

3. Suppose the robot cannot carry both mail and coffee at the same time, but the robot can carry a box in which it can place objects (so it can carry the box and the box can hold the mail and coffee). Suppose boxes can be picked up and dropped off at any location. Give the STRIPS representation for
2. Change the representation of the delivery robot world of Example 6.1 so that the robot cannot carry both mail and coffee at the same time. Test it on an example that gives a different solution than the original representation.
1. Consider the planning domain in Figure 6.1.(a) Give the STRIPS representations for the pick up mail (pum) and deliver mail (dm)actions.(b) Give the feature-based representation of the MW and RHM features.
• A partial-order planner does not enforce an ordering between actions unless there is a reason to make such an ordering.
• A planning problem for a fixed horizon can be represented as a CSP, and any of the CSP algorithms can be used to solve it. The planner may need to search over horizons to find a plan.
• A regression planner searches backwards from the goal, where each node in the search space is a subgoal to be achieved.
• A forward planner searches in the state space from the initial state to a goal state.
• Planning algorithms can be used to convert a planning problem into a search problem.
• An action is a partial function from a state to a state. Two representations for actions that exploit structure in states are the STRIPS representation, which is an action-centric representation, and the feature-based representation of actions, which is a feature-centric representation.
• Planning is the process of choosing a sequence of actions to achieve a goal.
18.(a) Explain why NASA may want to use abduction rather than consistency-based diagnosis for the domain of Exercise 17.(b) Suppose that an atmospheric disturbance dist could produce static or no signal in the low-bandwidth signal. To receive the static, antenna a3 and the spacecraft’s
17. Figure 5.15 shows a simplified redundant communication network between an unmanned spacecraft (sc) and a ground control center (gc). There are two indirect high-bandwidth (highgain)links that are relayed through satellites (s1, s2) to different ground antennae (a1, a2).Furthermore, there is a
16. Suppose you are implementing a bottom-up Horn clause explanation reasoner and you want to incrementally add clauses or assumables. When a clause is added, how are the minimal explanations affected? When an assumable is added, how are the minimal explanations affected?
15. Consider the bottom-up negation-as-failure proof procedure of Figure 5.11. Suppose we want to allow for incremental addition and deletion of clauses. How does C change as a clause is added?How does C change if a clause is removed?
14. Suppose you have a job at a company that is building online teaching tools. Because you have taken an AI course, your boss wants to know your opinion on various options under consideration.They are planning on building an intelligent tutoring system for teaching elementary physics (e.g.,
13. This question explores how integrity constraints and consistency-based diagnosis can be used in a purchasing agent that interacts with various information sources on the web. The purchasing agent will ask a number of the information sources for facts. However, information sources are sometimes
12. AILog has askables, which are atoms that are asked of the user, and assumables, which are collected in an answer.Imagine you are axiomatizing the plumbing in your home and you have an axiomatization similar to that of Exercise 2. You are axiomatizing the domain for a new tenant who is going to
11. Consider using abductive diagnosis on the problem in the previous question, with the following elaborations.• Valves can be open or closed. Some of valves may be specified as open or closed.• A valve can be ok, in which case the gas will flow if the valve is open and not if it is closed;
10. Deep Space One (http://nmp.jpl.nasa.gov/ds1/) was a spacecraft launched by NASA in October 1998 that used AI technology for its diagnosis and control. For more details, see Muscettola et al.[1998] or http://ti.arc.nasa.gov/tech/asr/planning-and-scheduling/remote-agent/ (although these
9. Consider the following clauses and integrity constraints:false ← a ∧ b .false ← c .a ← d .a ← e .b ← d .b ← g .b ← h .c ← h .Suppose the assumables are {d,e, f, g, h, i}. What are the minimal conflicts?
8. Suppose there are four possible diseases a particular patient may have: p, q, r, and s. p causes spots. q causes spots. Fever could be caused by one (or more) of q, r, or s. The patient has spots and fever. Suppose you have decided to use abduction to diagnose this patient based on the
7. Consider the following knowledge base and assumables aimed to explain why people are acting suspiciously:goto_forest ← walking .get_gun ← hunting .goto_forest ← hunting .get_gun ← robbing .goto_bank ← robbing .goto_bank ← banking .fill_withdrawal_form ← banking .false ← banking
6. This question explores how having an explicit semantics can be used to debug programs. The file elect_bug2.ail in the AILog distribution on the book website is an axiomatization of the electrical wiring domain of Figure 5.2, but it contains a buggy clause (one that is false in the intended
5. A bottom-up proof procedure can incorporate an ask-the-user mechanism by asking the user about every askable atom. How can a bottom-up proof procedure still guarantee proof of all (nonaskable)atoms that are a logical consequence of a definite-clause knowledge base without asking the user about
4. Consider the knowledge base KB:a ← b ∧ c .b ← d .b ← e .c .d ← h .e .f ← g ∧ b .g ← c ∧ k .j ← a ∧ b .(a) Show how the bottom-up proof procedure works for this example. Give all logical consequences of KB.(b) f is not a logical consequence of KB. Give a model of KB in which
3. Consider the following knowledge base:a ← b ∧ c .a ← e ∧ f .b ← d .b ← f ∧ h .c ← e .d ← h .e .f ← g .g ← c .(a) Give a model of the knowledge base.(b) Give an interpretation that is not a model of the knowledge base.(c) Give two atoms that are logical consequences of the
2. Consider the domain of house plumbing shown in Figure 5.13 In this diagram, p1, p2, and p3 are cold water pipes; t1, t2, and t3 are taps; d1, d2, and d3 are drainage pipes.Suppose you have the following atoms • pressurized_pi is true if pipe pi has mains pressure in it • on_ti is true if tap
1. Suppose we want to be able to reason about an electric kettle plugged into one of the power outlets for the electrical domain of Figure 5.2. Suppose a kettle must be plugged into a working power outlet, it must be turned on, and it must be filled with water, in order to heat.Write axioms in
• In choosing a representation, an agent designer should find a representation that is as close as possible to the task, so that it is easy to determine what is represented and so it can be checked for correctness and be able to be maintained. Often, users want an explanation of why they should
• To know when it has solved a task, an agent must have a definition of what constitutes an adequate solution, such as whether it has to be optimal, approximately optimal, or almost always optimal, or whether a satisficing solution is adequate.
• To solve a task by computer, the computer must have an effective representation with which to reason.
• A designer of an intelligent agent should be concerned about modularity, how to describe the world, how far ahead to plan, uncertainty in both perception and the effects of actions, the structure of goals or preferences, other agents, how to learn from experience, how the agent can reason while
• A physical symbol system manipulates symbols to determine what to do.
• An agent acts in an environment and only has access to its abilities, its prior knowledge, its history of stimuli, and its goals and preferences.
• Artificial intelligence is the study of computational agents that act intelligently.
• An intelligent agent requires knowledge that is acquired at design time, offline or online.
• Complex agents are built modularly in terms of interacting hierarchical layers.
• An agent has direct access to what it has remembered (its belief state) and what it has just observed. At each point in time, an agent decides what to do and what to remember based on its belief state and its current observations.
• Agents are situated in time and must make decisions of what to do based on their history of interaction with the environment.
• An agent is composed of a body and interacting controllers.
• Agents have sensors and actuators to interact with the environment.
• An agent system is composed of an agent and an environment.
• When graphs are small enough to store the nodes, dynamic programming records the actual cost of a lowest-cost path from each node to the goal, which can be used to find the next arc in an optimal path.
• Iterative deepening and depth-first branch-and-bound searches can be used to find lowest-cost paths with less memory than methods, such as A * , which store multiple paths.
• Multiple-path pruning and cycle pruning can be used to make search more efficient.
• A * search can use a heuristic function that estimates the cost from a node to a goal. If graph is not pathological (see Proposition 3.2) and the heuristic is admissible, A * is guaranteed to find a lowest-cost path to a goal if one exists.
• Breadth-first and depth-first searches can find paths in graphs without any extra knowledge beyond the graph.
• Many problems can be abstracted to the problem of finding paths in graphs.
• Optimization can use systematic methods when the constraint graph is sparse. Local search can also be used, but the added problem arises of not knowing when the search is at a global optimum.
• Stochastic local search can be used to find satisfying assignments, but not to show there are no satisfying assignments. The efficiency depends on the trade-off between the time taken for each improvement and how much the value is improved at each step. Some method must be used to allow the
• Arc consistency and search can often be combined to find assignments that satisfy some constraints or to show that there is no assignment.
• Constraint satisfaction problems are represented as a set of variables, domains for the variables, and a set of hard and/or soft constraints. A solution is an assignment of a value to each variable that satisfies a set of hard constraints or optimizes the sum of the soft constraints.
• Instead of reasoning explicitly in terms of worlds or states, it is almost always much more efficient for an agent to reason in terms of variables or features.
• A causal model predicts the effect of interventions.
• Consistency-based diagnosis and abductive diagnosis are alternative methods for troubleshooting systems.
• Abduction can be used to explain observations.
• Negation as failure can be used to make conclusions assuming complete knowledge.
• Proof by contradiction can be used to make inference from a Horn clause knowledge base.
• Bottom-up and top-down proof procedures can be proven to be sound and complete.
• A sound and complete proof procedure can be used to determine the logical consequences of a knowledge base.
• Given a set of statements that are claimed to be true about a domain, the logical consequences characterize what else must be true.
• A definite clause knowledge base can be used to specify atomic clauses and rules about a domain when there is no uncertainty or ambiguity.
• Representing constraints in terms of propositions often enables constraint reasoning to be more efficient.
13. Pose and solve the crypt-arithmetic problem SEND + MORE = MONEY as a CSP. In a cryptarithmetic problem, each letter represents a different digit, the leftmost digit cannot be zero(because then it would not be there), and the sum must be correct considering each sequence of letters as a base ten
12. Consider the constraint graph of Figure 4.16 with named binary constraints. r1 is a relation on A and B, which we can write as r1(A, B), and similarly for the other relations. Consider solving this network using VE.(a) Suppose you were to eliminate variable A. Which constraints are removed? A
11. Modify VE to count the number of models, without enumerating them all. [Hint: You do not need the backward pass, but instead you can pass forward the number of solutions there would be.]
10. Explain how arc consistency with domain splitting can be used to count the number of models.If domain splitting results in a disconnected graph, how can this be exploited by the algorithm?
9. Give the algorithm for variable elimination to return one of the models rather than all of them.How is finding one easier than finding all?
8. Modify arc consistency with domain splitting to return all of the models and not just one. Give the algorithm.
7. Which of the following methods can(a) determine that there is no model, if there is not one(b) find a model if one exists(c) find all models?The methods to consider are(a) arc consistency with domain splitting(b) variable elimination(c) stochastic local search(d) genetic algorithms.
6. Consider a scheduling problem, where there are five activities to be scheduled in four time slots. Suppose we represent the activities by the variables A, B, C, D, and E, where the domain of each variable is {1, 2, 3, 4} and the constraints are A > D, D > E, C ≠ A, C > E, C ≠ D, B ≥ A, B
5. Consider how stochastic local search can solve Exercise 3. You should use the “stochastic local search” AIspace.org applet or the book’s Python code to answer this question. Start with the arcconsistent network.(a) How well does random walking work?(b) How well does hill climbing work?(c)
4. Consider the complexity for generalized arc consistency beyond the binary case considered in the text. Suppose there are n variables, c constraints, where each constraint involves k variables, and the domain of each variable is of sized. How many arcs are there? What is the worst-case cost of
3. Consider the crossword puzzles shown in Figure 4.15.The possible words for (a) are:ant, big, bus, car, has, book, buys, hold, lane, year, ginger, search, symbol, syntax.The available words for (b) are at, eta, be, hat, he, her, it, him, on, one, desk, dance, usage, easy, dove, first, else,
2. Suppose you have a relation v(N, W) that is true if there is a vowel (one of:a, e, i, o, u) as the N-th letter of word W. For example, v(2, cat) is true because there is a vowel (“a”) as the second letter of the word “cat”;v(3, cat) is false, because the third letter of “cat” is
1. Consider the crossword puzzle shown in Figure 4.14.You must find six three-letter words: three words read across (1-across, 4-across, 5-across)and three words read down (1-down, 2-down, 3-down). Each word must be chosen from the list of 18 possible words shown. Try to solve it yourself, first by
13. The depth-first branch-and-bound of Figure 3.12 is like a depth-bounded search in that it only finds a solution if there is a solution with cost less than bound. Show how this can be combined with an iterative deepening search to increase the depth bound if there is no solution for a particular
12. Give a statement of the optimality of A * that specifies a class of algorithms for which A * is optimal. Give the formal proof.
11. Consider the algorithm sketched in the counterexample of the box.(a) When can the algorithm stop? (Hint: it does not have to wait until the forward search finds a path to a goal.)(b) What data structures should be kept?(c) Specify the algorithm in full.(d) Show that it finds the optimal
10. Bidirectional search must be able to determine when the frontiers intersect. For each of the following pairs of searches specify how to determine when the frontiers intersect.(a) Breadth-first search and depth-bounded depth-first search.(b) Iterative deepening search and depth-bounded
9. The overhead for iterative deepening with b − 1 on the denominator is not a good approximation when b ≈ 1. Give a better estimate of the complexity of iterative deepening when b ≈ 1. (Hint: think about the case when b = 1.) How does this compare with A * for such graphs?Suggest a way that
8. How can depth-first branch-and-bound be modified to find a path with a cost that is not more than, say, 10% greater than the least-cost path. How does this algorithm compare to A * from the previous question?
7. What happens if the heuristic function is not admissible, but is still nonnegative? What can we say about the path found by A * if the heuristic function(a) is less than 1 + ϵ times the least-cost path (e.g., is less than 10% greater than the cost of the least-cost path)(b) is less than δ more
6. The A * algorithm does not define what happens when multiple elements on the frontier have the same f-value. Compare the following tie-breaking conventions by first conjecturing which will work better, and then testing it on some examples. Try it on some examples where there are multiple optimal
5. Draw two different graphs, indicating start and goal nodes, for which forward search is better in one and backward search is better in the other.
4. This question investigates using graph searching to design video presentations. Suppose there exists a database of video segments, together with their length in seconds and the topics covered, set up as follows:Segment Length Topics covered seg0 10 [welcome]seg1 30 [skiing, views]seg2 50
3. Consider the problem of finding a path in the grid shown in Figure 3.14 from the position s to the position g. A piece can move on the grid horizontally or vertically, one square at a time. No step may be made into a forbidden shaded area.(a) On the grid shown in Figure 3.14, number the nodes
2. Which of the path-finding_ search procedures are fair in the sense that any element on the frontier will eventually be chosen? Consider this question for finite graphs without cycles, finite graphs with cycles, and infinite graphs (with finite branching factors).
1. Comment on the following quote: “One of the main goals of AI should be to build general heuristics applicable to any graph-searching problem.”
9. Suppose you have a new job and must build a controller for an intelligent robot. You tell your bosses that you just have to implement a command function and a state transition function. They are very skeptical. Why these functions? Why only these? Explain why a controller requires a command
8. Suppose the robot has a battery that must be charged at a particular wall socket before it runs out. How should the robot controller be modified to allow for battery recharging?
7. Change the controller so that the robot senses the environment to determine the coordinates of a location. Assume that the body can provide the coordinates of a named location.
6. The current controller visits the locations in the to_do list sequentially.(a) Change the controller so that it is opportunistic; when it selects the next location to visit, it selects the location that is closest to its current position. It should still visit all the locations.(b) Give one
5. If the current target location were to be moved, the middle layer of Example 2.5 travels to the original position of that target and does not try to go to the new position. Change the controller so that the robot can adapt to targets moving.
4. Consider the “robot trap” in Figure 2.11.(a) This question is to explore why it is so tricky for a robot to get to location g. Explain what the current robot does. Suppose one was to implement a robot that follows the wall using the “right-hand rule”: the robot turns left when it hits an
3. The obstacle avoidance implemented in Example 2.5 can easily get stuck.(a) Show an obstacle and a target for which the robot using the controller of Example 2.5 would not be able to get around (and it will crash or loop).(b) Even without obstacles, the robot may never reach its destination. For
2. Consider the top level controller of Example 2.6(a) If the lower level reach the timeout without getting to the target position, what does the agent do?(b) The definition of the target position means that, when the plan ends, the top level stops. This is not reasonable for the robot that can
1. The start of Section 2.3 argued that it was impossible to build a representation of a world independently of what the agent will do with it. This exercise lets you evaluate this argument.Choose a particular world, for example, the things on top of your desk right now.(a) Get someone to list all
5. Choose four pairs of dimensions that were not compared in Section 1.5.10. For each pair, give one commonsense example of where the dimensions interact.
4. For each of the Winograd schemas in Example 1.2, what knowledge is required to correctly answer the questions? Try to find a “cheap” method to find the answer, such as by comparing the number of results in a Google search for different cases. Try this for six other Winograd schemas of Davis

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