Re: SUO: Units of measure - representation of multipliers
On the question of precision:
There are several ways precision is expressed in
different contexts, and the way I think handles most
(probably not all) needs is to have a general
category of "quantifier" which is used together
with a unit of measure to represent a measurement.
A quantifier would then have as subclasses, in addition
to the usual set of numbers (integer, real, etc.)
several other classes such as "Range" (2-5),
"Distribution" (normal, Poisson, etc.), "Limit"
(<3.5), "Approximation" (ca. 3.50), and possible
others. An unqualified number could be considered
as exact or as having some default tolerance,
depending on the application.
In a real system I will expect that assertions about
things in the real world such as dimensions of
specific objects, or average dimensions of a class of
objects, will be enclosed in a wrapper indicating a number
of contextual variables related to the assertion --
e.g. the time or time interval that the assertion
is asserted to be true, the time the assertion was made,
the person making the assertion, its credibility, the
Reality context (fictional? hypothetical? consensus
reality?), and others. For measurements,
a default or specific tolerance can be part of the
wrapper as a slot, even if a seemingly precise number is
used.
The scientific convention of having the precision
related to the number of significant digits will be
important to use when interpreting scientific texts,
but for internal representations, it is not general
enough. I think that some specific conventions with
enough flexibility to handle the multiple ways people
talk about precision will be needed.
The multipliers used to relate units of measure
can also be represented by such quantifiers. An
unqualified number can indicate an exact (defined)
conversion factor, and number with a tolerance
would indicate a conversion factor dependent on
measurement.
Pat Cassidy
=========
Adam Pease wrote:
>
> Tim,
> Excellent point. Thanks for explaining further. We should indeed make
> precision explicit in the ontology as making things explicit is a key
> advantage of an ontology. Maybe one option for us would be to create a
> term NumberWithTolerance subclassed from Number
> <http://ontology.teknowledge.com:8080/rsigma/SKB.jsp?req=SC&name=Number&caseSensitive=on&skb=Merge>
>
> and a sketch of a definition would be as follows:
>
> (subclass NumberWithTolerance Number)
>
> (=>
> (instance ?NUMBER NumberWithTolerance)
> (exists (?PART1 ?PART2)
> (and
> (equal ?PART1 (NumberValueFn ?NUMBER))
> (equal ?PART2 (PrecisionFn ?NUMBER)))))
>
> We'd then need other axioms which state things like the fact that adding or
> subtracting from a number with a precision value that is larger than the
> number being added or subtracted results in no change in the first
> number. So, for example, if for the purpose of this email I show a number
> with a precision in the form (<number> <precision>p)
>
> (10 1p) + 0.5 = (10 1p)
>
> and
>
> (10 0.1p) + 0.5 = (10.5 0.1p)
>
> Maybe in fact there is a mathematics of numbers with precision. Has this
> been worked out for the mechanical engineering world where tolerances are
> critical?
>
> Do you have additional thoughts on this?
>
> Adam
>
> At 09:10 AM 8/17/2001 +0100, Tim King wrote:
>
> >Dear Adam,
> >
> >There is no distinction in the current representation between an exact and
> >an inexact multiplier. This has various other facets such as the
> >difference between a defined multiplier and a derived multiplier. Perhaps
> >I am coming at this ontology work from totally the wrong direction but I
> >am used to working with data models where making things explicit is an
> >important part of being able to share knowledge effectively. The main
> >difference I think I have understood is that in an ontology the framework
> >will allow greater derivation of knowledge that is not directly
> >stated. However, the representations within this framework can still be
> >used in a way that hides foundational knowledge. In the case of the
> >specific example in hand, I see no reference to the concept of integer in
> >representing the multiplier.
> >
> >I do not believe that, at the expense of accurate and robust modelling of
> >our world, the ontology should avoid "unwieldy", except in so far as we
> >attempt to mirror how human beings make some concepts simple for daily use
> >but have underlying richer models for more critical applications. I am
> >keen to know that we our vision includes both the house-wife's view of a
> >kilogramme of apples and the rocket engineer's view of a kilogramme of
> >fuel. However, both must be derivable from the same underlying framework
> >that corresponds to the ISO standard for SI units of measure and the use
> >(or otherwise) of the standard within the industrial contexts that lead to
> >both the experiences above.
> >
> >Cheers,
> >Tim.
> >
> > > -----Original Message-----
> > > From: Adam Pease
> > [<mailto:apease@ks.teknowledge.com>mailto:apease@ks.teknowledge.com]
> > > Sent: 16 August 2001 19:37
> > > To: Tim King; 'Dickert, John'
> > > Cc: standard-upper-ontology@ieee.org
> > > Subject: RE: SUO: RE: SUMO as a starter document
> > >
> > >
> > > Tim,
> > > I agree with you and believe that the authors are aware of
> > > this. The
> > > confusion arises because of an artifact with the ontology
> > > browser only. If
> > > you look at the ontology source file you'll find that Nano-Second is
> > > correctly listed as being 1.0E-9 of a Second even though the browser
> > > erroneously displays as 9.999999717180685E-10. While we
> > > certainly want the
> > > browser to be as accurate as possible and will fix this, it
> > > is intended
> > > only as an aid to understanding our proposal. The text
> > > source file should
> > > be considered definitive.
> > > On the other hand, you might instead be making a point
> > > about the number
> > > of digits which are considered significant in a conversion
> > > factor. One
> > > possible solution would be to have all numbers stated with all their
> > > significant digits. That could be unwieldy though for simple
> > > multipliers
> > > as I'm not sure how we'd represent that the notion of "doubling" has
> > > infinite precision (in terms of the multiplier itself). Was
> > > this the issue
> > > that you were addressing and do you have a suggestion as to
> > > how to solve it?
> > >
> > > Adam
> > >
> > >
> > > At 07:44 AM 8/16/2001 +0100, Tim King wrote:
> > >
> > > >I think you miss my point. I am well aware of the answer
> > > that you gave (I
> > > >should be stripped of my professional engineer status if I
> > > am not ;-) I
> > > >deduce that the proposers of the unit of measure ontology are not
> > > >aware. The current representation does not capture, make
> > > explicit and
> > > >preserve the richness that is enabled by the usual
> > > conventions of the
> > > >paper-based era.
> > > >
> > > >Cheers,
> > > >Tim.
> > > >
> > > >*************************************************************
> > > ************
> > > >*
> > > >* Dr. Timothy M. KING CEng MIMechE PhD DIC ACGI
> > > >* Executive Consultant, Technology
> > > >* LSC Group, Concept House, Victoria Road, TAMWORTH, UK - B79 7HL
> > > >* Switchboard: +44-1827-708000 Fax: +44-1827-708500
> > > >* Direct telephone: +44-1827-708535 (with VoiceMail)
> > > >* e-mail: tmk@lsc.co.uk Internet:
> > > ><<http://www.lsc.co.uk/>http://www.lsc.co.uk/>http://www.lsc.co.uk/
> > > >*
> > > >*************************************************************
> > > ************
> > > >
> > > >
> > > >
> > > > > -----Original Message-----
> > > > > From: Dickert, John
> >[<<mailto:JDickert@DTIC.MIL>mailto:JDickert@DTIC.MIL>mailto:JDickert@DTIC.MIL]
> >
> > > > Sent: 14 August 2001 21:53
> > > > To: 'Tim King'
> > > > Subject: RE: SUO: RE: SUMO as a starter document
> > > >
> > > >
> > > > 1E-9 has an error of measurement of 1 part in 1. 1.00E-9
> > > > has an error
> > > > of measurement of 1 part in 100.
> > > >
> > > > -----Original Message-----
> > > > From: Tim King
> > [<<mailto:tmk@LSC.CO.UK>mailto:tmk@LSC.CO.UK>mailto:tmk@LSC.CO.UK]
> > > > Sent: Wednesday, July 18, 2001 8:06 AM
> > > > To: Standard-Upper-Ontology (E-mail)
> > > > Subject: RE: SUO: RE: SUMO as a starter document
> > > >
> > > >
> > > > A very fine web reference; I will use this often, I think.
> > > > Thank you.
> > > > However, I also think that you are missing my point about the
> > > > string "1E-9".
> > > > Is it the same as "1.00E-9". On what basis have we chosen
> > > > this notation?
> > > > Is this representation sufficient for all possible forms of
> > > > mathematical
> > > > accuracy and determinism? If all systems implemented SUMO as
> > > > is would they
> > > > avoid the introduction of numerical error that the ontology
> > > > browser has
> > > > done? Furthermore, for instance, the conversion factor for
> > > > miles to meters
> > > > is "1609.344". I suppose that this is derived (from meter ->
> > > > inch -> foot
> > > > -> yard -> mile?). We are mixing up string representation of
> > > > numbers that
> > > > have a different foundation.
> > > >
> > > >
> >
> >Adam Pease
> >Teknowledge
> >(650) 424-0500 x571
>
> Adam Pease
> Teknowledge
> (650) 424-0500 x571
--
=============================================
Patrick Cassidy
MICRA, Inc. || (908) 561-3416
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