Lessons from the AI Midterms, Spring 2006

Prof. Futrelle - Northeastern University

On this page I discuss some of the difficulties that students experienced in taking the AI Midterms in the two courses, CSU520 and CSG120, this April 2006. Each bit of advice tells you about things you need to correct or at least pay more careful attention to when taking the Final. The notes should help you in taking the Final Exams, since they will go over much of the same ground as the Midterms.

The design of the Final Exams this semester will be to have a few more problems than the Midterm, but each will be easier than the most difficult ones on the Midterm. This applies to both the logic and uncertainty topics.

In taking an open-book exam, one suggestion I make to students is to make xerox copies of the most important material from the book. This can help avoid needless flipping through pages of your textbook looking for things. An example is the logical equivalences table, Fig. 7.11 in AIMA.

For logic, there were some serious difficulties with resolution theorem proving:

• Attempting to construct a proof that avoided resolution, even when explicitly required to use resolution.
• Successfully converting to conjunctive normal form but then not attempting to resolve clauses.
• Trying to resolve clauses "wholesale", when in fact only a single pair of literals should be resolved at each step. In CNF, a clause is a single literal or a disjunction of literals. A literal is an atomic sentence, a single propositional symbol, or the negation of an atomic sentence.
• Not paying careful attention to the equivalences between the universal and existential quantifiers, AIMA, page 252.
• Once you have created the clauses you will use, you can number each one in order. When you resolve a pair of literals to create a new clause, give it a new number. Then you're resolution proof can refer to the two numbers of the clauses you're resolving, the literals being resolved and the substitutions used.
• Skolemization: In first-order logic (FOL) Skolem constants are created in one step of the resolution process, when existential quantifiers are removed. It is only necessary to create Skolem functions when the variable involved when the existential quantifier occurs within the scope of a universal quantifier. Otherwise, you only need to create Skolem constants. See, for example, this Wikipedia entry, "Skolem normal form".
• In resolution in FOL, you need to do substitutions to unify variables between clauses. When you do these, write down what substitutions you are using. Standardizing apart variables will avoid confusion and ambiguities.

For uncertainty and probability there were also some difficulties.

• I did not and will not ask you to fully understand normalization. But, as on the Midterm, I may explicitly instruct you to use normalization, but I will explain how to use it if you are asked.
• Some failed to understand the basic relationship between joint probabilities and conditional probabilities.
• It is important to realize how marginal probabilities are computed by summing over the terms in the joint that are not represented in the joint. So if a joint involves A and B, P(A,B), then P(a) is computed by summing the joints across the two values of B, P(a) = P(a,b) + P(a,¬b).
• In doing Bayesian network problems some inadvertently omitted some of the terms in the sums and products needed to compute the joints from the CPTs.

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