   # Exam 1 Intro to Logic Programming & AIDue 2/23, start of class

Selmer Bringsjord

Name:

1. Write your name in the space provided above
2. Process your LSAT problem (which one designated by me; you will need to print it out):
1. give answers (mark the a, b, c, d, or e option for each question)
2. represent the problem and each question in first-order logic; give proofs for your answers in a natural deduction scheme
3. create input files to OTTER; obtain proofs from OTTER
4. collect (a)-(c) together in hard copy form
3. Answer the following True/False questions by checking the box of your choice
1. A formula in the propositional calculus is valid iff it is true on all truth-value assignments. Let be a formula of the propositional calculus. The question of whether is valid is mechanically (= algorithmically) solvable. True False

2. A formula in first-order logic is valid iff it is true on all interpretations, i.e., for all ,  . Let be a formula in first-order logic. The question of whether is valid is mechanically (= algorithmically) solvable. True False

3. Let be a set of formulas in the propositional calculus, and let be a formula in the propositional calculus. Then iff . True False

4. Let be a set of formulas in first-order logic, and let be a formula in first-order logic. Then iff . True False

5. Let be an inconsistent set of formulas in first-order logic. If this set if given as input to OTTER, and OTTER is allowed to run for any finite amount of CPU time t, OTTER is guaranteed to find a contradiction. True False

4. staple this sheet to other hard copy (for 2); initial next to your name above to indicate that you understand exactly why you have given the answers you have; submit   