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Adrian,
The great thing about numbers is there are so
many different sorts to choose from: Naturals, integers, rationals, reals,
complex, quarternons 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). I suspect if
you get into the hard maths, then that will raise questions about the axiom of
choice and whether you should use it. And, of course, you wouldn't be able to
axiomatise even the integers in many description logics, since they are designed
to prevent you describing problems that are undecidable.
Sean Barker
Bristol, UK
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Hi John,
You wrote
...anybody who needs a different
ontology for numbers can use that instead.
Somehow I'm reminded of
the saying "the nice thing about standards is that there are so many of them to
choose from"
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?
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:
http://www.economist.com/businessfinance/displaystory.cfm?story_id=15016132
Cheers, -- Adrian
Internet Business Logic
A Wiki and SOA
Endpoint for Executable Open Vocabulary English over SQL and RDF
Online at www.reengineeringllc.com
Shared use is free
Adrian Walker
Reengineering
On Thu, Dec 10, 2009 at 9:23 AM, John F. Sowa <sowa@xxxxxxxxxxx>
wrote:
Most people on this list understand the distinction between
form
and content, but some discussions tend to blur the distinction.
I
received an offline question related to that point, and I thought
it might
be useful to forward the answer to the list.
John
Sowa
___________________________________________________________________
>
May I know what is the difference between semantic network
> and
ontology?
A semantic network is a graphical form for knowledge
representation.
It can be used to express content of any kind.
An
ontology is a formal definition of content, which could be
represented in
many different KR languages and notations.
The distinction between form
and content is critical, but some
KR languages incorporate some ontology
into the basic notation.
Therefore, they would combine some content with
the form.
For example, a temporal logic is likely to have at least a
minimal
ontology for time built into the notation and rules of
inference.
A KR language that includes arithmetic will have an ontology
for
numbers and operations on numbers built into the basic
language.
Common Logic is a version of logic that is as neutral as
possible
about ontology. For example, CL includes syntax for
numerals, but
it does not assume any axioms about the integers represented
by
those numerals. One application might represent integers
of
arbitrary length, but another might have an upper limit of
2^63.
Some people have complained about the lack of an ontology
for
numbers in CL. But there are many different ontologies that
can
be added to CL as needed. One example is the Mathematical
toolkit
in the ISO standard for Z notation. It's a fine ontology,
it's
defined by an ISO standard, and anyone who wants it can use it
in
conjunction with CL. But anybody who needs a different
ontology for
numbers can use that instead.
John
Sowa
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