[CL] Modules in CL and CGIF

[John F. Sowa]

Chris,

I believe that I can make a stronger case for my claim
than you can for yours:

JS> For me, restricted quantifiers are the normal case,
 > and unrestricted quantifiers are only used in mathematics,
 > where the subject matter is limited to just one type of
 > entities.  If you specify the domain to be integers, you
 > won't expect quantifiers to range over cats and dogs.

CM> In my ontology, the prime numbers are chihuahuas.
 > I had to put the number 17 to sleep the other day...

But you're proving my point -- you really should adopt
restricted quantifiers even in mathematics when your
numbers start going to the dogs.

Three points:

  1. Historically, the first development of quantifiers
     -- Aristotle's syllogisms -- explicitly tied the
     quantifier to the domain (a special case, but one
     that still forms the backbone of the widely used
     description logics).

  2. In natural languages, nearly every quantified noun
     phrase has an explicit restriction on the domain of
     quantification; the few that don't usually have an
     implicit restriction that can be found in the context.

  3. In mathematics (which is the source of most examples
     of untyped quantifiers), mathematicians are very clear
     about stating an explicit universe that restricts the
     domain of all quantifiers.  If every quantifier has the
     same restriction (a very, very special case indeed), it
     is reasonable to omit it.

The fact that predicate calculus is untyped is a historical
accident:  it was developed primarily by mathematicians in
studies that used only one domain, such as chihuahuas.

John