GENERAL GROUND RULES
- The
exam will cover chapters 9-14 of LPL (pp. 227-374), plus the
handout on “Properties of Relations”
(online).
- The exam
is on Monday, December 10, 2007, 8:30 - 10:20 am.
- You must
bring a (purple) Standard Answer Sheet (“bubble-sheet”) and
#2 pencil. Do not use ink on the exam!
- Please
fill out your vital statistics (course name and number, your name, etc.)
on the bubble sheet before the exam. Include your section number
(AA, AB, etc.). If you need to look it up, be sure to do so. Fill in
the bubbles carefully so that your results get correctly credited to
you.
- You may
bring scratch paper, but no books or notes.
WHAT TO EXPECT ON THE EXAM
The format
will be multiple choice. On each question there will be only one correct
answer. On some questions, some answers may be partially correct;
but a partially correct answer will not be given partial credit. It is
never correct to fill in more than one “bubble” on the
answer sheet. You will receive zero credit for any answer on which more
than one bubble is filled in.
Topics to be covered are:
- Tarski
Worlds: You will need to be able to determine the truth-value of
a quantified FOL sentence in a particular world. (You will be looking
at pictures of Tarski worlds.) Since you will not have the TW program
running, you will have to figure this out on your own, without the benefit
of playing the game with TW.
- Fitch
proofs: Since you will not have Fitch running, you will not be required
to construct any proofs. But you will have to recognize and explain
the steps in an incomplete Fitch proof you will be shown. You will need
to provide justifications (rule and line citations) if they are missing,
or provide the steps (if they are missing) based on rule and line citations
and on subsequent developments in the proof. In working these problems,
you are strongly advised to try filling in the missing lines,
etc., on the exam sheet before answering the questions. Try to understand
the proof before making your choices.
- Informal
proofs: You will be presented with some informal proofs and asked
to evaluate them. You should recognize which strategies are being used
(proof by cases, proof by contradiction, general conditional proof,
universal generalization, existential instantiation). If the proof is
correct, you should recognize it as such. If it contains a mistake,
you should be able to identify the mistake.
- Translation:
There will be a lot of emphasis on translations on this exam, including
numerical quantification. You will be given English sentences and be
asked to select the correct FOL translation, and vice versa. You will
need to be aware of different equivalent ways of translating from English
to FOL, and vice versa. Sometimes there is more than one correct answer,
and sometimes not.
- Equivalence:
You will need to be able to determine whether or not a pair of FOL sentences
you are presented with are equivalent. This will come up in a context
in which you are presented with a number of pairs of sentences and asked
to pick out the equivalent pairs. For help in recognizing equivalent
sentences, print out a copy of the file Some useful
quantifier equivalences. (You can’t bring it with you to the
exam, though!)
- Different
kinds of necessity: You will be asked to place various sentences
in an “Euler” diagram like the one on p. 272. So you should know the
difference between tautologies, FO-validities, logical truths, and TW-necessities.
- Theory:
Some questions will test your understanding of concepts such as the
following: wffs vs. sentences, free vs. bound
variables, the truth-functional form of a quantified FOL
sentence, vacuously true generalized conditionals, soundness
of system F,
completeness of system F,
properties of relations (symmetry, reflexivity, etc.), infinite
domains, Russell’s theory of descriptions and Strawson’s
criticism of it. Memorizing definitions will not be adequate —
you will need to understand the concepts and how they are interrelated.
Now it’s
time to put your study to work. Take the practice
quiz on theory, equivalence, and translation. If you find that you can’t read all of the
logical symbols on the quiz, you may need to add a font to your computer.
To get the font you need, click here.
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