Intro to Logic Programming & AI

**Selmer Bringsjord**

**Name**:

- Write your name in the space provided above
- Process your LSAT problem (which one designated by me; you
will need to print it out):
- give answers (mark the a, b, c, d, or e option for each question)
- represent the problem and each question in first-order logic; give proofs for your answers in a natural deduction scheme
- create input files to OTTER; obtain proofs from OTTER
- collect (a)-(c) together in hard copy form

- Answer the following True/False questions by checking the box
of your choice
- 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

- 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

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

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

- 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

- A formula in the propositional calculus is
- 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

Wed Feb 18 08:34:38 EST 1998