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C00002 00002	charni[e85,jmc]		Comments on Charniak and McDermott
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charni[e85,jmc]		Comments on Charniak and McDermott

The discussion of representation in ``predicate calculus'' should
mention

1. The terminology used by logicians, since many students will also
take courses in logic.  This includes "pure predicate calculus", first
order logic, second order logic, type theory.

2. The decision among (red x) and (color x 'red) can be based on
whether one may subsequently want to quantify over colors.
Likewise using (inst table-1 table)  suggests that we may want
to use some rules of the form  (all (x y) (if (inst x y) ...)).

When one explains symptoms by a disease, as on p. 22, one wants  p
such that  p ⊃ q, where  p  has certain other intensional properties,
e.g. it is of the form "x has a certain disease" and one also requires
that  p  not be obviously inconsistent with other known facts.

p.23 - It isn't obvious how the semantic net notation goes beyond
binary predicates.  Even though it has been proved that all n-ary
predicate calculus can be reduced to binary predicates, it isn't
necessarily a good idea.

p.322 - 
Making formulas denote propositions is on the right track for the
reasons you give, but then having terms
denote individuals is inconsistent with compositionality at least if you
want a formula

(knows pat-7 (telephone mike-7))

and we don't want

(knows pat-7 (telephone mary-22))

just because Mike and Mary live together unbeknownst to Pat.
It is better to make terms denote individual concepts.

Also it isn't clear what happens when the formula contains variables,
especially if you want to put quantifiers on the variables.
Consider

(believe john-22 (mortal x)),

where for simplicity we assume that the variable  x  ranges over men.
We can want to put quantifiers on it in two ways.  The easiest is
to say

(all (x) (believe john-22 (mortal x)))

i.e. for every man John believes he is mortal.  This might be true,
but suppose John believed that Perseus was a god and hence immortal
although Perseus is actually a man.  Then it would be false.  The
other way of quantifying gives

(believe john-22 (all (x) (mortal x))),

which stands for ``John believes all men are mortal'', something
that we also want to be able to say.

My own proposal is to introduce ``inner variables'' which are constants
as far as the outer logic is concerned.  We may use doubled letters
to denote them.  Using them

(mortal xx)

is not a proposition but an ``innner propositional form''.
We also have a function  alll  where we triple the L.

(alll xx (mortal xx))

is the proposition that all men are mortal, and we can have

(believe john-22 (alll xx (mortal xx))).

The key virtue of this idea is that since  alll  is an ordinary
function as far as logic is concerned we can axiomatize its
properties.  However, this gets us in deeper, because in order
to do so we need variables ranging over inner variables which
range over men.  Let's use doubled capital letters for them.

We can then have the true formula