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Exam 1
Intro to Logic Programming & AI
Due 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 tex2html_wrap_inline33 be a formula of the propositional calculus. The question of whether tex2html_wrap_inline33 is valid is mechanically (= algorithmically) solvable.
      tex2html_wrap_inline37 True
      tex2html_wrap_inline37 False

    2. A formula in first-order logic is valid iff it is true on all interpretations, i.e., for all tex2html_wrap_inline41 , tex2html_wrap_inline41 tex2html_wrap_inline45 . Let tex2html_wrap_inline33 be a formula in first-order logic. The question of whether tex2html_wrap_inline33 is valid is mechanically (= algorithmically) solvable.
      tex2html_wrap_inline37 True
      tex2html_wrap_inline37 False

    3. Let tex2html_wrap_inline55 be a set of formulas in the propositional calculus, and let tex2html_wrap_inline57 be a formula in the propositional calculus. Then tex2html_wrap_inline59 iff tex2html_wrap_inline61 .
      tex2html_wrap_inline37 True
      tex2html_wrap_inline37 False

    4. Let tex2html_wrap_inline55 be a set of formulas in first-order logic, and let tex2html_wrap_inline57 be a formula in first-order logic. Then tex2html_wrap_inline59 iff tex2html_wrap_inline61 .
      tex2html_wrap_inline37 True
      tex2html_wrap_inline37 False

    5. Let tex2html_wrap_inline55 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.
      tex2html_wrap_inline37 True
      tex2html_wrap_inline37 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




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Selmer Bringsjord
Wed Feb 18 08:34:38 EST 1998