Midterm Key

1. Which of the following is the best example of emergent behavior in a search-based chess program? (choose one)
   1. The design of the chess program (e.g. selecting a search algorithm).

      This is barely a behavior, and it hardly emerges from the mechanistic operation of obvious tactical principles.

   2. The implementation of the chess program (e.g. coding in C).

      See previous choice.

   3. The specific tactics exhibited by the chess program (e.g., choosing a specific capture)

      No, the tactics are the programmed behavior.

   4. The general strategy exhibited by the chess program (e.g. choosing to `go on the defensive'.)

      Yes, this is an example of a complex behavior emerging from simple tactical principles.

2. Briefly argue that a thermostat is smarter than a rock.

   A thermostat has an appropriate reaction to its environment. Key words here were `reactive', `sensing and behavior', etc.

3. Name three sub-disciplines of artificial intelligence which are current areas of research.

   A partial list might include these from the notes: Agents, Cognitive Modeling, Constraint Satisfaction, Game Playing, Human-Computer Interaction, Knowledge Representation and Reasoning, Boolean Satisfiability, Case-Based Reasoning, Computational Complexity of Reasoning, Decision Theory, Logic, Nonmonotonic Reasoning, Ontology, Reasoning About Actions And Time, Spatial Reasoning, Uncertainty, Machine Learning and Data Mining, Natural Language Processing and Information Retrieval, Planning and Scheduling, Robotics, Search

4. Consider a robot in a 1-dimensional grid-space world (a line). Each end of the grid has a barrier, and somewhere on the grid may be a goal. An example state in such a system:

   

   Let the robot be able to sense the following conditions
   • LG --- true when a goal is to the left
   • RG --- true when a goal is to the right
   and have the following actions
   • LM --- move to the left
   • RM --- move to the right
   • HP --- halt and powerdown
   1. Give a reactive system in the style of Nilsson which will halt the robot on top of the goal if present, and will never run into a barrier.

        LG   -> LM
        RG   -> RM
        true -> HP
      

      Many folks gave more complicated but equivalent systems.

   2. Give a CNF propositional formula in terms of the sensor variables which completely describes the conditions under which your last action of the previous answer will be executed.

      not LG and not RG

      Looking for CNF, and for the condition. For those who wrote the last rule with this precondition, this was easy :-).

5. Which of the following are valid statements of or about propositional logic? (choose all that apply)
   1. A or not A derives not A or A
   2. A and not A derives A
   3. A or not B entails A
   4. A and not B entails A
   5. A and not B entails B
   6. A and not A implies A ~~~ (As in the text, implies is the `implies' operator.)

   Most folks seemed confused about (b), so I made it a one-point extra credit. Another major source of confusion was (f): write the truth table here.

6. List all the models of A or not A

   A = \TRUE, A = \FALSE. A model is a binding of truth values to atoms of the formula which makes the formula true. It is not a true formula. An exhaustive set of literals was accepted as well.

7. Consider the following search tree.

   

   Which of the following statements hold? (choose all that apply)
   1. In a depth-first search of this tree, node 3 is visited for the first time before node 5 has been visited?
   2. In a breadth-first search of this tree, node 3 is visited for the first time before node 5 has been visited?
   3. In an iterative-deepening search of this tree, node 3 is visited for the first time before node 5 has been visited?

8. In a two-dimensional grid space world, let the Maximal Manhattan Distance (MMD) from a point \langle x_1, y_1 \rangle to a point \langle x_2, y_2 \rangle be twice the horizontal (x) distance or twice the vertical (y) distance, whichever is larger, i.e.

   MMD = 2\cdot \max(|x_2 - x_1|, |y_2 - y_1|)

   Thus, in this figure

   

   the MMD from (a) to (b) is 2\cdot \max(2, 3) = 6.

   What property of MMD makes it not an admissable heuristic for solving sliding tile puzzles using A* search?

   It sometimes overestimates the distance to a goal, potentially pruning parts of the search which contain the minimum-cost solution. This is different from monotonicity.

9. Rewrite the following first-order formula as an equivalent propositional formula:

   exists x \in \{1, 2\}.A(x) or not B(x)

   A_1 or not B_1 or A_2 or not B_2

   Close answers to this got partial credit.