Symbolic Logic

phone 877-4483

Web page

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Office hours: M 12:00-2:00, TTh 9:30-12:00;

other times by appointment.

August 29, 2003

This course assumes you have taken and passed CSC/MTH 156 (``Discrete Structures'').

Logic is a way to come to know a fact without observing it directly. If your roommate always gets drunk on Saturday nights, and today was Saturday, you don't have to smell your roommate's breath to know that (s)he is drunk. There are, of course, many more subtle applications of logic, and frequently it's not so obvious what conclusions you can draw from what. The careful study of this question, and the field of logic itself, dates approximately to Aristotle. Aristotle's treatment of logic was so widely respected that the field changed little for two thousand years, until the 19th century when mathematicians like Boole, Frege, Peano, and Peirce cleaned it up to roughly its present state.

Since logic, like other branches of mathematics, has trouble dealing with ambiguous statements, and since English is a notoriously ambiguous language, logicians (and other mathematicians) usually work in a language of their own, in which every term and symbol has a clear, well-defined meaning -- the ``language of first-order logic'', or FOL as the textbook calls it.

We'll start by examining *relations*, properties that can be
either true or false of specific objects. Relations can be combined using
*Boolean connectives* such as ``not'', ``and'', ``or'',
``implies'', and ``iff'' (short for ``if and only if''),
and we'll discuss how to use, prove, and
disprove statements involving those connectives. Then we'll add
*quantifiers* to the language, so we can talk about ``all'' objects
or ``at least one'' object, and discuss how to use, prove, and disprove
statements involving quantifiers. Finally, we'll visit some topics of
particular importance in computer science: mathematical induction
and, if we have time, computer theorem-proving
(which underlies the Prolog programming language).

The main text for this course is *Language, Proof and Logic*,
by Jon Barwise and John Etchemendy. We'll work through most of chapters
1-13, plus part of chapter 16, by the end of the semester.
**You are responsible for everything
in the reading assignments, whether or not I discuss it in a lecture.**

The textbook comes with a CD-ROM
containing not only the full text of the book but a number of software
packages which you'll need in order to do your homework. The software
should run on either Macintosh or Windows; you may use whichever you
prefer. One of the software packages, ``Submit'', requires Net access
to submit your homework to an automatic grading program; an option in
the program allows you to submit the homework to me for a grade, or to
just check it so you can see what's incorrect and fix it *before*
submitting it for a grade. Printed on the CD-ROM envelope is a ``Book
ID#'', which you'll need in order to use the auto-grader, so don't lose
it. *Note:* the Book ID# is *non-transferrable*, so if you buy
a used copy of the book, you probably won't be able to submit your homework
to the autograder. In other words, *don't buy a used copy of the
book!*

I expect you to have read the specified chapters in the textbook
*before* the lecture that deals with that topic; this way I can
concentrate my time on answering questions and clarifying subtle or
difficult points in the textbook, rather than on reading
to you, which will bore both of us. **Please read ahead!**

As I write this, I plan to give several homework assignments, a midterm exam, and a final exam, as well as a ``brownie point'' grade which is my subjective impression of how seriously you're taking the course. The midterm and the ``brownie points'' are each weighted the same as a homework assignment, and the final exam is equivalent to two homework assignments, in determining a semester grade. You earn brownie points by asking good questions in class, coming to me for help when you need it, etc. You lose brownie points by cheating, by being lost and not doing anything about it, and by annoying the professor.

The exams must be taken at the scheduled time, unless arranged in advance or prevented by a documented medical or family emergency. If you have three or more exams scheduled on the same date, or a religious holiday that conflicts with an exam or assignment due date, please notify me in writing within the first two weeks of the semester in order to receive due consideration. Exams not taken without one of the above excuses will get a grade of 0.

Homework assignments will be accepted late, with a penalty of 20% per 24 hours or portion thereof after they're due. An hour late is 20% off, 25 hours late is 40% off, and after five days it gets a zero. Any homework turned in after the last day of class will get a zero.

Most of the assignments in this class are to be done individually. You
may *discuss general approaches* to a problem with classmates, but
you *may not copy* large pieces of homework solutions.
If you do, *all* the students involved will be penalized.

All work on an exam must be entirely the work of the one
person whose name is at the top of the page. If I have evidence that
one student copied from another on an exam, *both* students will be
penalized; see above.

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