Re: Issues about contexts and quantifiers
Date: Fri, 9 Apr 93 15:16:13 -0400
Message-id: <>
Subject: Re:  Issues about contexts and quantifiers
Cc: interlingua@ISI.EDU, jfulton@ISI.EDU
> ....  But a problem arises when the variables nested
> inside the quoted statement refer to something quantified outside
> the quote, as in the sentence "There is are two blocks A and B,
> and Tom believes that A is on B."  If we consider both A and B
> to be proper names, there is no problem:
>    (and (block A) (block B)
>         (believes Tom `(on A B) )
> But consider a related sentence that requires variables:
> "For any blocks ?a and ?b, if ?a is on ?b, then Tom believes
> that ?a is smaller that ?b."  To represent this sentence, we need
> a comma in front of the nested variables to force them to be
> evaluated to show the coreference with the ?a and ?b outside the
> quotes:
>    (forall ((?a block) (?b block))
>            (=> (on ?a ?b)
>                (believes Tom `(smaller_than ,?a ,?b)) ))
> However, Mike said that a simple comma is not sufficient and
> that the last line of this statement should be
>                (believes Tom `(smaller_than ,(name ?a) ,(name ?b))) ))
> The reason for the extra "name" functions is that ,?a would refer
> to an actual physical block, and a physical thing cannot be present
> inside a belief.  But ,(name ?a) would produce a lexical identifier
> that could occur inside a belief.
> However, I was not happy with that analysis....

A hidden premise in the above argument appears to be that the object
of "believes", in a KIF representation of a belief sentence, needs to
be a CLOSED formula. I want to question that assumption, and ask why
we shouldn't simply write

    (forall ((?a block) (?b block))
            (=> (on ?a ?b)
                (believes Tom `(smaller_than ?a ?b)) )),

without resort to commas or "name" functions. Note that in specifying
the truth conditions of
    (tau believes phi),

(where tau and phi are terms, with the denotation of phi being a
formula) under a given interpretation and variable assignment, we can
perfectly well make reference to the semantic values of variables
occurring in the formula that is the denotation of phi under that
interpretation and variable assignment. Those of course are the same
values that those variables have throughout the scopes of the
quantifiers binding them.

The desire to make phi denote a closed formula perhaps is motivated by
the idea that our semantics for (tau believes phi) will say something
like "the individual denoted by tau has the sentence denoted by phi in
his knowledge base (as an explicit assertion)". But this is hardly
plausible anyway. Even if we assume that believing is a matter of having
explicit formulas in the head, it is unlikely that other agents can be 
assumed to have exactly the same internal vocabulary as we (or arbitrary
KIF KBs!) do; so we ought to allow that a proposition WE can express as 
(smaller_than A B) would be internalized by another agent as 
(smaller_than' A' B') where the primed symbols differ arbitrarily from 
the unprimed ones. Indeed, the other agents may believe this proposition
without having it explicitly stored in their heads at all. For instance,
most of us probably believe, but do not have explicitly in out heads, 
that dogs are wingless. 

Rather than making strong assumptions about formulas in the head,
it seems to me that what we want to say about (tau believes phi) is
that the PROPOSITION expressed by the formula denoted by phi is in
the belief set of the individual denoted by tau. And while this
leaves open the problem of what exactly propositions are, the crucial
point is that an open formula can perfectly well express a proposition
(under a given interpretation and variable assignment). 

Am I missing the point?

Len Schubert