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Re: [ontolog-forum] Form and content

To: <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "sean barker" <sean.barker@xxxxxxxxxxxxx>
Date: Thu, 10 Dec 2009 20:49:56 -0000
Message-id: <05CA40A89FE142DEB2E06849880A0F92@SMB>
    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


From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Adrian Walker
Sent: 10 December 2009 15:20
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Form and content

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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:


                         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

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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