From: Chris Welty <cawelty@gmail.com>

Date: Wed, 18 Feb 2009 22:07:44 -0500

Message-ID: <499CCD00.6070309@gmail.com>

To: Alan Ruttenberg <alanruttenberg@gmail.com>

CC: Sandro Hawke <sandro@w3.org>, public-rif-wg@w3.org, Boris Motik <boris.motik@comlab.ox.ac.uk>, W3C OWL Working Group <public-owl-wg@w3.org>

Date: Wed, 18 Feb 2009 22:07:44 -0500

Message-ID: <499CCD00.6070309@gmail.com>

To: Alan Ruttenberg <alanruttenberg@gmail.com>

CC: Sandro Hawke <sandro@w3.org>, public-rif-wg@w3.org, Boris Motik <boris.motik@comlab.ox.ac.uk>, W3C OWL Working Group <public-owl-wg@w3.org>

Alan, I'm afraid I'm not able to follow your line of reasoning. I was not suggesting there is a single way to interpret representations of numbers, quite the opposite. You have mentioned "mathematical properties" as if it is some Platonic ideal, however the phrase is so general as to mean anything. In fact, in any possible interpretation I can think of, disjointness is a mathematical property, one that we have proposed to apply to e.g. integers and floats. And clearly "being and integer" and "being a float" are mathematical properties, I don't know what else they could be. So, yes, let's define things based on their mathematical properties? That can't be it - so either we agree or I don't know what your talking about and I can't even respectfully disagree - how about respectfully confused. -Chris Alan Ruttenberg wrote: > On Tue, Feb 17, 2009 at 11:05 PM, Chris Welty <cawelty@gmail.com> wrote: >> Alan, >> >> As I mention on our call, there are plenty of scientists and engineers who >> will dispute your abstract notion of "mathematical properties of numbers". >> Floats and decimals *are* different, and represent different things. For >> example, when a float represents a measurement taken with a certain >> precision, then it is simply *not the case* that 1.0000^^xs:float == >> 1^^xs:decimal. They really are not the same. > > Hello Chris, > > Jos and I had an extended discussion of this particular issue - about > "Imprecise" numbers and I believe that he agreed this to be a > misnomer. What you say is equally true of decimal numbers - if an > number represents an approximate measure then using it as a precise > number is wrong. Imprecisions arise from different situations and are > not a property of the numbers themselves. The specification of > floating point numbers does not say that each represent a range of > numbers, or an approximate number. Both the float and decimal > specification say that each series of bits represent an exact number. > > It is in the movement to the real world to these numbers, such as in > measurement, or in some types of operations on the numbers, that > imprecision is introduced. For example the specification of decimal > says that there is implementation specific rounding applied when > operations might result in numbers with more digits of precision than > are supported by the implementation. This introduces imprecision in a > manner analogous to the way that some floating point operations do. Or > consider a measurement is approximated to the 100th of an inch as a > decimal. > > Alternative uses of the hardware arithmetic units, and alternative > designs for hardware emphasize that precision is a fluid concept - > integer units are used for floating point operations and vice versa, > and recently it has been proposed that for certain types of operations > (such as decoding streaming media) precision of operations even on > integers could be traded off for lowered power consumption. > > So I must respectfully disagree with your assessment here. While there > very well may be *some* engineers and scientists that think of > floating point numbers in the way you suggest, there is not a single > way in which floating point numbers are used nor a single way in which > decimal numbers are used. The representation issue you mention is not > unique to floating point numbers, either in their specification, or in > their use. I remain of the opinion that the proper way to specify > machine representations of numbers is to define their behavior in > terms of their mathematical properties. > > -Alan > > >> It is true that the RIF decision was motivated much more by the need to >> comply with our existing implementation base, however that base is itself >> grounded in very real science and engineering, and very real and practical >> understanding of the mathematical properties of numbers. >> >> >> -Chris >> >> >> Sandro Hawke wrote: >>> My take on this: RIF justifies the choice of making xs:float and >>> xs:decimal disjoint on the basis that this is needed in order for >>> implementations of RIF to be based on existing implementation of xpath >>> operators. The consequences of this choice for OWL go beyond simply >>> making the types disjoint but bring addition constraints on types of >>> facet values and additional complexity due to the possibility of >>> implementation dependent results for the numeric operators. The >>> adoption of xpath operators brings forward a number of issues that seem >>> inadequately considered and this choice may turn out to be unworkable, >>> in practice, even for RIF. >>> >>> In order for OWL to be precisely defined we need to base our >>> specification on the mathematical properties of numbers, not the >>> properties of implementations. >> -- >> Dr. Christopher A. Welty IBM Watson Research Center >> +1.914.784.7055 19 Skyline Dr. >> cawelty@gmail.com Hawthorne, NY 10532 >> http://www.research.ibm.com/people/w/welty >> > -- Dr. Christopher A. Welty IBM Watson Research Center +1.914.784.7055 19 Skyline Dr. cawelty@gmail.com Hawthorne, NY 10532 http://www.research.ibm.com/people/w/weltyReceived on Thursday, 19 February 2009 03:08:32 GMT

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