CIS630 Homework 3: Propositional and Predicate Logic

Due: Wednesday, November 1 at 11:59 p.m.
1 point late penalty for each minute late

For notational convenience, you can spell out 'ForAll' and 'Exists' if you're using a text editor that doesn't support the logic symbols. Also, you can use & for 'And' and ~ for 'Not'.

  1. (15 points) Express the following statements in Propositional Logic:
    1. D is true only when S is.
    2. Either R is true, or both S and T are.
    3. Tim is a student but Mark is not (define the proposition symbols you use).
  2. (20 points) Derive the indicated statements using inference rules for propositional logic: The KB initially contains:
    1. (H & ~J) -> (P -> Z)
    2. R & (J -> S)
    3. ~S
    4. R -> H
    5. S v P
    • derive: H
    • derive: Z
    • derive: ~(S v ~P)
    • derive: J -> Z
  3. (32 points) Rewrite the following statements in FOL, stating definitions for the predicates you use:
    1. Fred is a tiger.
    2. Tigers growl.
    3. The Columbus Zoo is a zoo.
    4. The Columbus Zoo has a tiger.
    5. Every zoo has at least one tiger.
    6. Some zoo has a tiger that is bigger than all other tigers.
    7. Every person who meets a tiger is scared of it.
    8. Zoos that have tigers but not lions are unpopular.
  4. (13 points) Do problem 9.4 from the book.
  5. (20 points) Given the following statements:
    1. Everybody who John likes, likes John.
    2. Jim likes only people that John likes.
    3. Jim likes Jane.
    Prove using resolution that someone likes John.

    Submission instructions:

    Write up all of your answers in a text editor so that it can be submitted electronically. Submit only text or pdf files. Put all of the files you want to submit, and ONLY those files, in a directory on STDSUN, and use the submit command to send the files to the grader. The syntax of the submit command is:

    > submit c630aa lab3 (lab3_dir)

    Where lab3_dir is the directory containing the files you want to submit. You can learn about using the submit command by typing man submit at a unix command prompt. If you cannot get the submit command to work, you can email your files to the grader, but please don't use this option unless you're having trouble with submit.