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RE: Relating mathematics to XML -- using properties for enabli

• From: "Len Bullard" <Len.Bullard@ses-i.com>
• To: "Costello, Roger L." <costello@mitre.org>,<xml-dev@l...>
• Date: Wed, 25 Jul 2012 08:08:14 -0500

What is the infoset?

There are variations of this in features analysis.  Another question is
how do languages (as graphs or networks of associated features) become
modular to adapt to semantic drift?  There are some clues here:

http://www.technologyreview.com/view/428504/computer-scientists-reproduc
e-the-evolution-of/

len

-----Original Message-----
From: Costello, Roger L. [mailto:costello@mitre.org] 
Sent: Wednesday, July 25, 2012 8:00 AM
To: xml-dev@lists.xml.org
Subject:  Relating mathematics to XML -- using properties for
enabling understanding

Hi Folks,

I think mathematics is fascinating.

I learned recently that in mathematics it is not the particular symbols
that matter, but rather that the symbols (whatever they may be) exhibit
the desired properties such as commutativity and associativity.

For example, the plus sign ( + ) is usually the symbol used to express
addition, but other symbols could be used. In fact, in mathematics
"terminology and notation are individual and often idiosyncratic." [1]

Despite no standardization of symbols, mathematics is considered the
universal language.

Wow!

Why is that? What enables understanding even in the midst of different
terminology and notation?

I think it's the properties -- such as commutativity, associativity, and
identity -- that enable understanding. If we use different symbols but
our properties are the same, then we are probably talking about the same
thing.

For example, suppose I tell you that I have an operator @ that has these
properties:

    a @ b = b @ a                                for any a, b

    a @ (b @ c) = (a @ b) @ c            for any a, b, c

    a @ 0 = 0 @ a = a                          for any a

then you probably understand that I am talking about the addition
operation.

Now let's see how this applies to XML.

Here is the title of a (fabulous) book: 

    Category Theory for Computing Science

I may mark up that title like so:

    <Title>Category Theory for Computing Science</Title>

But clearly with markup "terminology and notation are individual and
often idiosyncratic." That is, you may mark up the same data like this:

    <Name>Category Theory for Computing Science</Name>

How shall we understand each other, given our different terminology?

Perhaps there is a lesson from mathematics -- use properties for
enabling understanding.

But does markup have properties? What properties might there be for the
above example?

/Roger

[1] "Category Theory for Computing Science" by Michael Barr and Charles
Wells, p. xvi.

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• References:
  • Relating mathematics to XML -- using properties for enablingunderstanding
    • From: "Costello, Roger L." <costello@mitre.org>