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C00002 00002	commen.226[w83,jmc]	Comments on student papers
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commen.226[w83,jmc]	Comments on student papers

J. P. Bion
	The point of the exercise was to write out a plausible
set of axioms from which the desired conclusion really follows,
My 1958 formulation was defective, and it can be fixed using
situations.  You should still write out some axioms, because it
will make you limit yourself to a small precise set of ideas.

	The considerations you mention concerning the need for
formalizing a principle of choice are correct.
My candidate for this will involve non-monotonic reasoning to
be discussed later in the course.  That's why I haven't discussed
it yet.  It will come out nicely that if there is only one
known way of doing something then it should be used.

	As discussed in class, there was a bug in my revised
axioms in that they permit infinite dithering, in this case
walking back and forth between the desk and the car.  In class
I proposed to fix this by introducing a memory of a plan, so
that unless something to change it has occurred one should
continue with a previous plan.

Wesley Witte

	There needs to be some prose explaining the meaning of
the functions and predicates.  I was unable to figure out enough
to comment fully.  Yoram evidently did better.

	Your use of $x as a variable to mean that the variable
if universally quantified is dubious, especially in the
sentence 

1 Want(At (I, Airport), $Sx) 

which seems to mean that I will always want to be at the airport.
Of course, this helps with the present problem in an ad hoc way,
since in all the intermediate situations in this problem, presumably
I continue to want to be at the airport.  Perhaps this
can be handled by whatever general mechanism we use for the
frame problem.

In general innovations in the predicate calculus notation are a bad idea
in the solutions to exercises.  Predicate calculus took years to
debug, and the probability of a mistake in a new notation is high,
and the chance of being misunderstood is high.  It is better to
have a clear idea of what a first order language is and to use it.

It has been remarked in class that there is a conflict between
the requirements of the frame problem and making  at  transitive.

Quiz problem:  What is this problem and how is it to be resolved?

Ans: The frame problem requires that we give some way of asserting
what doesn't change when an event (action in this case) occurs.
If I am at the car and the car is at home then transitivity would
give that I am at home.  If my frame axiom says that when an object
moves all other at relations are conserved, then it will still be
deducible that I am at home when I have driven the car to the
airport.  We fix this by dividing at into two predicates, an immediate
at1(x,y,s) which is directly modified by actions and is not transitive
and a secondary at2(x,y,s) which is transitive.
They are related by ∀x.at1(x,y,s) ⊃ at2(x,y,s).