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CSC 165            Homework Exercise 2 -- Marking Scheme        Winter 2009
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NOTE TO STUDENTS:

You will find below the marking scheme used for your homework, including
the meaning of marking codes and number of marks associated with each one.
This file also contains my instructions to the marker (so you can get an
idea of how the homework was marked) and the marker's comments about each
question.

Please take the time to read this carefully before you ask questions about
the grading of your homework.


NOTE TO MARKER:

Be picky!  On any homework, it is the responsibility of students to show
that they understand how to solve each problem and to write up their
answers carefully.  At the same time, keep in mind that exercises are worth
only 2% of the final grade, so your marking should be somewhat coarse.  And
remember that marking is not only about evaluating a student's performance,
but also mostly about giving them feedback so that they can learn from
their mistakes.  This is especially important for students who made
numerous or more serious mistakes, as they are likely to need more feedback
in order to understand why their answers were incorrect.

For each question, I list solution elements with an associated code for
writing on student papers (the letter(s) between underscores _) and a
number of marks.  There are also general errors (with associated codes)
given below, with a maximum number of marks to take off for each type of
general error (as a percentage of the value of the question).  You will
likely encounter other common errors, or maybe decide to break down the
marking scheme further.  Simply make note of these changes/additions to
the marking scheme, and introduce new code letters (or short words) to
allow you to quickly give accurate feedback to the students (both in terms
of what they did wrong and how many marks it cost them).  Your marking
comments will be included in this marking scheme and posted on the course
website so that students may look up the meaning of marking codes and
understand how their work was marked.


GENERAL ERRORS (marked negatively, in addition to any other errors):

    _N_otation [up to 20%]:  incorrect/ambiguous notation

    _V_agueness [up to 20%]:  incorrect/unjustified/vague claim


1.  [10 marks]

    For each statement:

    _S_tandard [1 mark]:  correct "standard" representation (with all
        quantifiers over P)

    _N_on-standard [1 mark]:  correct "non-standard" representation
        (with quantifiers over sub-domains, or structure significantly
        different from "standard") -- give this for part (d) if they supply
        only one symbolic representation

    Marker's Comments:

    1c: This is not a biconditional, as not all Python programs are
        necessarily incorrect.  Also, you cannot assume the existence of a
        incorrect program based on this statement, so
        "\exists x in P, not J(x) and not T(x)" is incorrect.

    1d: For the purposes of this exercise, you were supposed to follow
        class notes and not use a quantifier.  However, interested students
        can look up how definite descriptions are translated into
        first-order predicate logic by philosophers and logicians
        (Wikipedia has a good article), and the philosophical issues that
        such a translation raises.

2.  [10 marks]

    For each statement:

    _M_eaning [1 mark]:  correct English meaning

    _N_aturalness [1 mark]:  English statement is *not* simply a
        word-for-word translation of the symbols (e.g., "for all programs,
        if the program is correct, then the program is written in Java",
        which would lose this mark)

    Marker's Comments:

    2b: The most common mistake was that people started with "Every program
        in Python" or something to that effect.  This statement says
        something about *all* programs, not just those in Python.

    2e: You had to be very careful with your wording for this question.
        "All Java programs are correct or incorrect." was not sufficient,
        because that sentence is ambiguous -- it could mean either all Java
        programs are correct or incorrect individually, or it could mean
        that they collectively are all correct or all incorrect.  Only the
        latter interpretation is correct.  Also, many people used the
        "either ... or ..." construction to connect the two parts of this
        symbolic sentence.  While that was accepted in this case because
        the two parts joined by the disjunction are contradictions of each
        other, in general, this would not be correct.  "Either ... or ..."
        in natural language is sometimes used for exclusive or, meaning the
        entire conjoined expression is true if and only if exactly one of
        the two is true, whereas the disjunction is an inclusive or, which
        is also true when both parts are true.