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Re: Relating mathematics to XML -- using properties forenablin

• From: John Cowan <cowan@mercury.ccil.org>
• To: David Carlisle <davidc@nag.co.uk>
• Date: Wed, 25 Jul 2012 10:30:54 -0400

David Carlisle scripsit:

> Not at all: you just have operations from for a commutative semigroup 

A commutative monoid, in fact, since there is an identity element.

> @ could be any operation at all where a and b are elements of the group
> and 0 is its unit. So it could be multiplication for example, the unit
> for multiplicative groups are normally written as 1 but as you noted
> "other symbols could be used" and 0 is just as good a symbol.

Quite so.  To pin down addition, you have to do a good deal more work;
the obvious starting point is the Peano axioms.

> What does this mean for XML? Not much, other than terms mean what they
> are defined to mean in the given context, and if you take them out of
> context they don't mean anything:-)

It is possible to define terms out of context, but not without
considerable pain.  In $EMPLOYER's ontology, for example, "attorney" is
defined as equivalent to "has at least one bar association ID number",
and bar associations are defined by enumerating them.  No doubt this
definition is U.S. parochial and will have to be fixed eventually.

-- 
We call nothing profound                        cowan@ccil.org
that is not wittily expressed.                  John Cowan
        --Northrop Frye (improved)

• References:
  • Relating mathematics to XML -- using properties for enablingunderstanding
    • From: "Costello, Roger L." <costello@mitre.org>
  • Re: Relating mathematics to XML -- using properties forenabling understanding
    • From: David Carlisle <davidc@nag.co.uk>