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THIS IS FOR IDEAS TO SHORT FOR INDIVIDUAL FILES

jan 15
	Barwise, in his perception class today, took for granted
but later defended against my criticism, making a new logic rather
than using first order logic.  We agree that if first order logic
were to be used, it would be necessary to introduce new entitities,
e.g. scenes, as objects of the language.  I regard this as good,
because it clarifies what we are talking about, and he regards it
as bad, because of a desire for ontological parsimony.  Moravcsik
decried a "bloated ontology", to which I said that I proposed to call
it an "enriched ontology".  Later Barwise and I agreed that I could
prove my case if I could find some useful functions from scenes to
objects, and I recalled the usefulness of functions from things
to concepts of them.  Barwise evidently intends to introduce scenes
as part of the semantic description of his language of perception.

	Here are some possibilities for expressions using scenes as
objects that might habilitate them.

	1. Scene1 is clearer than Scene2.

	2. The scene that would result from putting a lion into
Scene1.

	3. There is a scene in which a lion and a unicorn fight.

	4. Few notice the mushrooms in scenes containing lions unless
they are very large.

	The above examples are not really very good.

jan 15

	I would feel much more confident about starting a project
on the advice taker if we had a domain and a declarative formalism
entirely adequate for that domain, so that sophisticated problem
solving of the common sense sort could be entirely carried out in
the domain.  What about situations with people who have to be convinced
to change their views about something?  Could we play the role of
Galileo trying to persuade people that Jupiter had satellites.

jan 23

	There was a discussion today of whether mental qualities
should be ascribed individually.  One point that came up in a
discussion with Pat Hayes goes

Hayes: Discussions of philosophy are irrelevant to a theory of vision
needed to construct a robot that can print a description of a scene.

jmc: Maybe so, but it is more relevant to a robot that can reason about what
other entities know on the basis of what it observes about their
opportunities for seeing.

	Actually, commitments to empiricism still infect AI to its
detriment.  Namely, computer vision theories are often based on the
idea that objects are patterns of sense data and don't take into
account the fact that objects are patterns in the world not all
parts of which can be sensed and that a learning program must
infer such patterns.

jan 24

Anthropologists today seem to be infected by the ideology of the
peoples they study.  They don't seem to distinguish between their
correct ideas and their superstitions.  This presumably prevents
their studying the effects of the conflicts between native ideas
and reality and the corrective effects of their contact with
civilization.

jan 27

If we want to use numerical methods to determine the qualitative
behavior of differential equations and to prove the results, we
have to put in some analytical work somewhere, e.g. to obtain a
bound on some higher derivatives by analytic means.  Consider for
example a system

	x' = f(x,y)

	y' = g(x,y)

where the ' denotes differentiation with respect to t, and suppose
we want to prove that a there is exactly one limit cycle which we
have located by some numerical method.  In order to prove that it
is unique we might make one calculation in its vicinity to prove that
it is attractive.  This involves evaluating a certain integral along
the cycle, and our confidence in the result of numerically evaluating
the integral depends on having bounds for the derivatives of the
functions f and g.  Away from the limit cycle we may want to show
that the solution curves cut a certain family of ovals in the right
direction.  This will also involve proving that certain functions
are postive on the ovals which can be shown by evaluating them at
enough points and using a bound on their derivatives.  This bound
can either be found numerically or it can itself be the result
of a numerical computation whose verification requires an analytically
obtained bound on higher derivatives.  The goal of the theory
should be to minimize the amount of analytical work by using
a program that combines much computation with a small amount of
analysis.

[I phoned Golub about this who referred me to Bob O'Malley 328-8763,
a visitor to the math dept.  O'Malley suggested that I look at
a paper by Charles Conley et. al. in the Indiana Journal of Math.
called something like "Invariant Regions" or "Sets" and also suggested
the proceedings of an AMS conference on non-linear oscillations edited
by Hoppenstadt.  He said the applications were mainly to population
oscillations.]

jan 29

Circumscription and intensionality

	The discovery that substitutivity of equals for equals doesn't
apply in opaque contexts comes as a surprise to most people, so
we would like a formalism which doesn't distinguish opaque from
transparent contexts linguistically and an axiom that says that
substitutivity is applicable except when there is an obstacle.
We apply circumscription to the predicate ⊗isobstacle, and when
there is no apparent obstacle we conclude that substitutivity is
possible.  In the case of knowledge, the obstacle is that the
second argument of  ⊗know occupies an opaque context.  We propose
something like

	%2equal(x,y) ∧ P(x) ∧ ∀z.¬prevsub(x,y,P) ⊃ P(y)%1.

	Well that's not very satisfactory, because it ⊗prevsub is
second order and also too specialized.  So we need another way of
realizing the idea.

Going down

	Suppose we are using a predicate ⊗knows(person,proposition), and
we make an iron clad rule that ⊗proposition cannot contain
⊗knows.  We can still use second level knowledge by inventing a
function ⊗knows1, axiomatizing it with the properties of ⊗knows needed
in the task at hand and allowing it to be an object of the original
⊗knows.  Instead of going up as is usual in making higher level logical
systems, we go down.  I suspect that going down may prove more
logically tractable.
	We, Walt Disney Productions, worry that maybe
some people think real people can fall off buildings and crash through
walls and get better after the injuries.  Maybe they are surprised
when they hit or push people and they often are crippled for the rest
of their lives.  Mary Roe here was pushed downstairs 20 years ago
and has been like this ever since.  Real people can't take it like
Popeye can.  Be careful with them, and they'll be careful with you
maybe.
Can we put all these together?

second order definitions
approximate theories
non-monotonic reasoning
partial models
bodies of knowledge
metamathematics by going down
cartesian product and tree counterfactuals
intensional circumscription

design before construction
generalized patterns
wants(Karla, hasaffair(Bill, wife George))

should be unambiguous unless there is some reason to the contrary