For your information, I include a slightly edited version of a message which expressed my sentiments on the Senate 'decisions'.

The guidelines as being promoted are already out of date and inadequate.

- I know, and my students know, that they never fit the particular situation in one of my courses.
- I know, and my students know, that the entire construct:
decisions made 'during the first week after the strike';
is a fantasy world.
- It will be at least a week after the end of a strike before my students even KNOW what marks they achieved on work submitted up to the beginning of the strike.
- I know, and my students know, that the first week will either be chaos of many undone class tests, presentations, and new material for exams - or a complete farce in which very few attend and many scramble to get work previously submitted accepted for full credit.
- Many students have been 'off work' for three weeks (or more) and one week does not resume momentum. They will be utterly unprepared for any 'regular' exam' - as they usually are for deferred exams.

The current guidelines basically apply *if* we have completed 65% of the
graded work, and you know the results of this work. We have only completed
either 50% (or 30% if the final had turned out to be better for you). Unless we
are given better options or more creative solutions, some additional work is
required.

Assignment 7 is due the first day after the strike. Unless you have major questions, you should just put it into the assignment box on North Ross 5th floor. There will not be any additional assignments.

Even if we have a full week of classes at the end of the strike, we will *not * cover new material in class - in terms of any class test or final exam.

People who need to leave town soon should contact me. Check out the page of information for Ganong's students and see if you wish to write his version of a final exam. With my permission, he will admit you to the exam and that work will be counted as our final would be.

With this in mind, I propose an option of an 'essay/written presentation' worth 30% of the grade. This can replace the class test - but is both more work and more learning. It is also something *you * can control the timing of!. Do some reading, some talking, some writing (minimum 10 pages typed double space).

The core task is to demonstrate that you read some additional logic,
and understood the key points (concepts) of the topic.
I will not expect
you to display actual proofs of theorems (such as completeness, soundness
etc.) but you should indicate the definitions for words you use.
I have a general page about the standards
I apply in marking such projects.

The essay will be due 15 days after the end of the strike (unless you apply for deferred standing). If you choose, you can submit an essay as a set of Web pages - and send me the URL!

Group projects are fine - but should be longer (15 + pages) and more complex. Here are a few topics which I have though of - but you can suggest others.

- The incompleteness of Peano Arithmetic.
We have heard about the completeness of propositional logic and of the predicate calculus. Peano Arithmetic is a theory for the natural numbers (including basic induction). What does incompleteness mean? Who proved it and, roughly, how? I understand that Turing machines are discussed in a second year course. What is the connection between this incompleteness and the undecidability of the halting problem of Turing Machines?

- The completeness of the theory of the real numbers.
Unlike the theory of natural numbers, there is a theory for real numbers which is complete and decidable. Describe this theory and what completeness means. Describe something about the decision procedure. What connection does this have with real work in mathematics and in computer science?

- Second-order logic.
We have been doing first-order predicate logic. This means there are many things we might like to talk about but cannot express. [For example, infinite sequences, and statements like: 'there is an infinite sequence such that ... '.] What does a second order logic system look like? Does computer science require second order logic? Are there things that second order logic cannot express?

- Alternate logics.
There are logics, such as intuitionist logic and constructivist logic, which deny some of the rules we have accepted. These deny the double negation rule (which means they deny \not elimination). These appear in modern computer science when you insist that something exists

*only*if you have an algorithm for constructing it. Describe one such system - and its connection to other parts of mathematics or computer science. - Temporal Logic
Temporal logic is another logic which is used in Computer Science. This logic includes a variable for time - t and propositions are true at time t0 or false at time t0. There are operators such as 'sometimes true' 'eventually true', 'never true', 'always true'. (These are clearly related - the negation of always true is sometimes true!)

Present a basic temporal logic with the added rules for these operators. Describe how it appears in some part of computer science (e.g. safety systems for Nuclear reactors!) - Fuzzy Logic
Fuzzy logic replaces the simple truth functions with two values T or F (or equivalently range {0,1}) with more general functions with range the whole interval [0,1]. What do you do with negation, conjunction, disjunction, conditionals, etc.? How is this used?

Several students have indicated there are web sites on this topic which could be a good place to start. If you use web sites, be sure to give me the URL.

- Logic Programming.
Look ahead to courses involving logic programming. What of the work we did does this build on? What other logic do you need for logic programming? In this context does it matter if your system is incomplete? Would it matter if your system was unsound?

Here is a reference from a CS prof on logic programming:

Malpos PROLOG a relational ... - Program verification.
Texts, such as the 2320 text, contain small sections of program verification. This includes writing critical information (specifications, etc.) about a program in the form of propositions, and then proving certain other properties continue to hold when the steps of the program are complete. write up a careful analysis of how (and what) logic is used in simple verifications. Working carefully through the section in the Math 2320 text, with additional comments on where this all leads, could be sufficient.

- The Satisfaction Problem for Propositional Logic.
This is a central example of a problem which is NP (has no algorithm which decides the answer in a time complexity which is polynomial in the size of the input). How do you compute the complexity of this problem? How are other 'hard' problems reduced to this example? Is it computationally feasible to use truth tables to decide general problems? Is the Satisfaction Problem decidable?

- Another question you have - which you should verify with me.
Contact me by e-mail [ whiteley@mathstat.yorku.ca] or see me on the picket line (see below).

(No I don't get phone messages). If you do not have regular access to e-mail, include your phone number and I will get back to you. In general, I can be found on the Shoreham Picket Line (Shoreham gate - behind the new six rink arena) on the morning shift - 8:00 - 11:00.

As an aside, if you are interested, just for the learning, we (on the picket lines) are
discussing a **YUFA FREE SCHOOL**. If this started, I will work with a seminar on Thinking with Diagrams. [A number of faculty from at least four departments have expressed an interest.] Let me know if you want to be kept informed about such a seminar! It may happen this summer, even after the strike is over.

Walter Whiteley

email address: whiteley@mathstat.yorku.ca

Department of Mathematics and Statistics.

York University