[SCL] new draft

[John F. Sowa]

Frank,

As you have noted, Z is a more complex language than CL.
But that compexity is designed to restrict the expressive
power of the language by ruling out possible statements
that are likely to be incorrect or ill advised.  Those
restrictions, however, also make it impossible to state
many kinds of statements that are legitimate in certain
circumstances.

 > Regarding "CL semantics is a superset of Z semantics",
 > my memory of your presentations then and since have been
 > the opposite: CL is a subset of Z, not a superset.
 > Besides, can you tell me what is a subset or superset
 > in this context?

By superset, we (meaning Pat, Chris, and me) mean that
the number of possible statements that can be made in CL
includes all possible statements that can be made in Z.
In other words, every statement that can be expressed
in Z has an exact translation to CL, but many statements
in CL (and the languages that CL is designed to support)
cannot be translated to Z.

 > (FYI, since CL is incompletely defined, I guess it supports
 > anything, right?  Or are there some real differences?)

Not true.  The CL semantics has been very precisely defined
for a long time.  Chris Menzel wrote a succinct version
in a highly technical form that only a professional in the
field of mathematical logic could understand.  We all agreed
to that semantics, but we realized that Chris's document
was not intelligible for a wider audience.

Pat Hayes has been working with the W3C to use the same
semantics as a foundation for RDF and OWL.  That experience
has given him a better feeling for the kind of terminology
and notation that would be acceptable.  He is now rewriting
Chris's specification in a more intelligible form.

Following are some kinds of statements that can be made
in CL, but not in Z.  I have stated them as informal English
sentences that could be translated to CL, but not to Z:

  1. Statements that have variables that range over relations,
     as in the formal translations of the following sentence:

     "Every relation in database X must have a fixed number
     of columns."

  2. Statements that violate type constraints:

     "Any statement that compares a dog to a number is false."

  3. Metalevel statements about statements in some language:

     "The following statement is illegal:  '(add dog cat)'."

Statements of these kinds, which can be stated in CL, can be
made in various logic-based languages that CL is designed to
support.  However, the strict typing constraints of Z make it
impossible to translate them to Z.

 > ... the past 40 years have taught us that typing is a Good Thing.

Certainly.  We agree with you.  However, different languages
have different rules about what kind of typing is supported
and what kinds of statements are legal or illegal.  Z happens
to have a very strict version of typing.  Therefore, any language
X with a different or a less strict kind of typing cannot be
translated to Z because many legal statements in X are not
legal in Z.  But statements in X can be translated to an untyped
language, such as SCL core.

JS> It is possible to translate Z to SCL, but it is not possible
 > to translate  SCL, CL, and many other logic-based languages to Z.

FF> I don't believe any of the above until I see it demonstrated.

Fine.  We're writing the demonstration now.  It will all be crystal
clear in the version we present in May.

JS> For the proposed CL standard, we plan to include an annex that
 > shows how Z can be translated to CL.  That translation would
 > make Z a CL-conformant language.

FF> For what purpose?

For the purpose of demonstrating what you said that you wanted
to see demonstrated.

FF>  All other (terminological) discussion is unfocused and likely
 > to be less productive.

We all agree on the fundamental principles.  We are merely arguing
over what words to use for the unwashed.  Tanel suggested that
we adopt a neutral term, such as "SCL text" until somebody can
suggest a better one.  I said "Amen, let's get on with it."

FF> Well, why not write down a strawman set of concept-term pairs
 > for the Definitions Clause that you anticipate in the 2004-04 draft?

That has been written.  It's Chris Menzel's document, which is much
stronger than straw -- it's made of gallium arsenide.  We're now
trying to make it intelligible.

John