Rich, Ferenc, Adrian, Sean, (01)
Form and content are not vague notions. When we are talking about
a language, a logic, or a knowledge representation system of any
kind, they are two sharply distinguished issues. (02)
RC> The distinction between form and content depends on what you
> consider form and what you consider content. Clear definitions
> of what constitutes form, and what comprises content, are missing. (03)
I thought it was obvious. In any case, (04)
Form: The pattern of symbols used to make a statement. (05)
Content: The subject matter and the propositions stated about
that subject. (06)
RC> But a different choice of background leads to... (07)
The distinction between the foreground and background of the subject
matter addresses two different aspects of the content. You can also
talk about aspects of the notation that are used to signal foreground
or background, but those are aspects of the form that is used in
a conventional way to point to aspects of the content. (08)
FK> In this context form and content are interchangeable... (09)
No. I can replace the grammar of a logic and get a notation that looks
totally different -- say predicate calculus or conceptual graphs --
and make exactly equivalent statements. But if you replace the content,
you're talking about something totally different. (010)
JFS>> ...anybody who needs a different ontology for numbers can use
>> that instead. (011)
AW> Somehow I'm reminded of the saying "the nice thing about standards
> is that there are so many of them to choose from" (012)
Certainly. There will never be a universal standard for everything,
since different applications with different problems and technologies
will require very different tools and representations. There is no
upper limit to the number of useful standards. (013)
AW> Seriously, if we can't agree on a standard for something as basic
> as a number, what are the chances for interoperability without the
> need for expensive and continuing human intervention? (014)
That question is unrelated to the conditional clause. We have had
interoperable computer systems for half a century. But all versions
of interoperability are task dependent. It's impossible to have
some kind of abstract, universal, task-independent interoperability. (015)
Even human beings, with the full flexibility of human intelligence,
are only capable of collaborating successfully on a limited number
of tasks without going through a lengthy period of training. (016)
Theoretically, Peano's axioms define the common notion of number. But
the number of applications that use integers of arbitrary size (e.g.,
the infinite precision Bignum in LISP) are extremely limited. The
overwhelming choice for applications is to use integers modulo some
suitable upper value: 2^1, 2^8, 2^16, 2^32, or 2^64. (017)
AW> To get a measure of how far there is still to go on this journey,
> here's a real world problem description that serves as a nice
> example of an interoperability requirement... (018)
The financial system is an excellent example. Double-entry bookkeeping
and the basics of banking services were developed during the Italian
Renaissance. The terminology for banking services is fairly universal.
Banks have been able to do electronic funds transfers and other kinds
of interactions for many decades. (019)
But... (and this is a big *BUT*) whenever two banks merge (which they
often do), they *never* merge their databases. Instead, they always
adopt one of two procedures: (020)
1. They continue to run the software and databases from *both* banks
for the accounts that came from those banks. (021)
2. They close the accounts of one of the parent banks, transfer the
funds to the other bank, and reopen new accounts in that bank. (022)
Usually, they adopt procedure #1 in the initial stage of the merger
and gradually use repeated applications of procedure #2 to convert
accounts. Nothing that we have ever discussed in this forum will
make any difference in that merger process. (023)
SB> The great thing about numbers is there are so many different sorts
> to choose from: Naturals, integers, rationals, reals, complex
> quaternions and so on, not to mention the modulo groups, the
> transfinite numbers and the floating point numbers (which, not
> being a metric space, make a mess of most theorems about numbers)... (024)
All of these are useful for various purposes, and more of them will
be invented in the future. Every one of them will be needed by
somebody somewhere for some application. (025)
John (026)
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