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C00002 00002	Hayes's comments on CONCEP[s78,jmc] @ 15 April 1977
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Hayes's comments on CONCEP[s78,jmc] @ 15 April 1977

Wants new versions of this and also minima.

He would like to see a model of the axioms.  What axioms?  It would
be nice to have a theory, and maybe I'll develop a full set of
axioms, but these are just a few randomly chosen properties, more or
less appropriate for the examples given.  Nevertheless, it wouldn't
be difficult to give a model of the axioms so far.
The elements of the model would be equivalence classes of expressions
like the Herbrand models of logic.  Because I have given few rules
which allow concluding that two expressions denote the same concept,
it would be very close to using the expressions themselves as elements
of the domain.

I agree with his idea that we need many concepts.  This takes two
forms.  First, there are many ways of designating the same telephone
number, e.g. "Telephone Mike" and "Telephone Mary".  Second, I mention
"a dog's concept of the location of here puppies".  However, it putting
this first, Hayes is giving a philosophical rather than an AI criticism.
From a philosophical point of view, it is easy to say that the
theory should be elaborated, and this can be done, but the AI problem
is to make use of even one version in a working program.  Therefore,
my current interest is in how to bring some such theory into a
practical form, i.e. to elaborate it to an axiom system that permits
a conclusion that a goal can be achieved.

2. He is right to worry about the value of Stanford.  It seems to me
that in the present form of the theory we have to say that no-one
knows Stanford, and no-one knows another person.  We can only know
a concept that has a value in some simple domain.  Not knowing
Stanford doesn't prevent us from knowing many concepts that
contain Stanford such as Statecontaining(Stanford) and not knowing Pat Hayes
doesn't prevent me from knowing Universitynamewhereworks(PJH).  This
should be spelled out in the paper, an it was lazy of me not to
mention that in the paper since I knew it at the time.

3. In general, Telephone Mike requires a more elaborate treatment
than I gave, because the concept is not completely well defined
on account of the empirical fact that a person may have many
telephone numbers.  One question is whether I can give such a
more elaborate treatment in my theory, and I think I can - modulo
the discussion of approximate concepts in my "Ascribing Mental
Qualities ...".  The second question is whether the kind of treatment
given in the concepts paper is useful for telephone numbers or in
other circumstances.  I will answer yes to both questions.  A machine
that was determined about the simple theory in which each person had
a unique telephone number would be useful in limited contexts.  However,
a really good machiee could use approximate theories without being
destroyed when the situation transcended their usefulness.  This is
a different AI problem which I hope can be studied somewhat separately.

4. p.2 Whatever Telephone John may be, it is not (his concept of)4154974430.
The mappings from objects to concepts are special and are not the
main notion of concepts.  Your concept of John's telephone is
not the result of applying some mapping to the telephone number.

5. I don't see that sillyexists satisfies (12), because it
is true for imaginary orange trees and Exists is not.

6. I may want your 20a,21a 22a also.

7. You are right that I need - among other things - assertions
that everyone knows the axioms of propositional calculus.  Clearly
I need a disclaimer about attemptng any kind of completeness.
I was more interested in examples of expressiveness than in trying
to achieve completeness.

8. p.8 - As I implied above, I would not be offended if you found
an interpetation in which the concepts are expressions.  The purpose
of the generalization is that they need not be expressions.  Moreover,
if I make And commutative, then you will be forced either to use
canonical forms, e.g. identify the concept with the equivalent
expression that comes first in alphabetical order, or to use
equivalence classes.

9. I don't want the rule of necessitation, because I don't want to
deal only with theorems but also with contingent facts.  In order
to avoid it, I suppose I have to strengthen the axioms somewhere
else.

10. You're probably right in your suggested improvement to (73).
Actually neither my formulation nor yours does justice to the
possibility that Peter really doesn't ascribe a precise length
to the yacht but merely thinks it will fit in his station wagon
when it won't.

11. As above, my axioms are mere samples of the truth and completeness
isn't asserted.  I probably won't get into trouble with consistency unless I
try for something like trying to prove the consistency of the theory
within itself.  After all, Goedel's work has a positive aspect too.  He
showed that many metamathematical concepts, e.g. provability could
be axiomatized - just not completely.