CS156 Fall 2017Practice Midterm 2

Studying for one of my tests does involve some memorization. I believe this is an important skill. Often people waste a lot of time and fail to remember the things they are trying to memorize. Please use a technique that has been shown to work such as the method of loci. Other memorization techniques can be found off the Wiki Page for Moonwalking with Einstein. Given this, to study for the midterm I would suggest you:

• Know how to do (by heart) all the practice problems.
• Go over your notes at least three times. Second and third time try to see how much you can remember from the first time.
• Go over the homework problems.
• Try to create your own problems similar to the ones I have given and solve them.
• Skim the relevant sections from the book.
• If you want to study in groups, at this point you are ready to quiz each other.

The practice midterm is below. Here are some facts about the actual midterm: (a) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (b) You should bring photo ID. (c) There will be more than one version of the test. Each version will be of comparable difficulty. (d) One problem (less typos) on the actual test will be from the practice test.

1. Give the backtracking-search algorithm for CSP's. Explain what forward checking is.
2. Directly use the definition of entailment to show `(A ^^ B) ^^ C |== A`.
3. Consider the statements about a possible Wumpus world:
   1. `neg W_{1,1}`
   2. `S_{1,1} <=> (W_{1,2} vv W_{2,1})`
   3. `S_{1,2} <=> (W_{1,1} vv W_{2,2} vv W_{1,3})`
   4. `S_{2,1} <=> (W_{1,1} vv W_{2,2} vv W_{3,1})`
   5. `neg S_{1,1}`
   6. `neg W_{1,2}`
   7. `neg W_{2,1}`
   8. `S_{1,2}`
   9. `neg S_{2,1}`
   Give a natural deduction proof of `W_{1,3}` from the above.
4. Give an example of each of the following: (a) a valid formula, (b) a satisfiable formula that is not valid, (c) an unsatisfiable formula.
5. (a) Write down the true table for `A = MIN(A,B,C)` where `A,B,C` are propositional variables. (b) express `A = MIN(A,B,C)` as conjunctive normal form formula using the procedure from class.
6. Give a resolution refutation for the set of clauses `{{A}, {bar{C}}, {bar{A}, B},{bar{B}, C} }`.
7. Briefly define each of the following terms and then give an example where they are different: (a) closed world assumption, (b) open world assumption.
8. Explain step-by-step through the code how the DPLL algorithm would work on the set of clauses `{{A}, {bar{A}, B},{bar{B}, C} }`.
9. Give a single first-order model satisfying all of the following sentences:
   1. `(exists x) K\i\ng(x)`
   2. `(exists x) (Person(x) ^^ \neg K\i\ng(x))`
   3. `(forall x) (K\i\ng(x) => Person(x))`
10. Give some additional rules of inference which might be used in a first-order proof, but which are not available in a propositional natural deduction proofs.