From: Michael Schneider <schneid@fzi.de>

Date: Fri, 3 Apr 2009 12:31:30 +0200

Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0011DA631@judith.fzi.de>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

Cc: <public-owl-wg@w3.org>

Date: Fri, 3 Apr 2009 12:31:30 +0200

Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0011DA631@judith.fzi.de>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

Cc: <public-owl-wg@w3.org>

Hi Peter, I see a lot of "no"s to all of my statements, but I am not quite certain that I understand your arguments. Do you claim that a set such as S := { 1, <2,3>, <4,5,6> } is allowed to be a subset of the data domain? I mean, where "<,>" is not just some random way to write down composite data values (such as the "/" in terms like "2/3" for expressing rationals), but it is really meant to be the n-tuple operator appearing in statements such as <x,y> in DR ? Or, more generally, do you say that all n-ary data ranges (or better, their "value spaces") must be subsets of the data domain? Let me say that I would not be particularly happy with this sort of "ontological mixup" (what about sets like "{ 1, {2}, {3,<{4,<5,6>}},7>}, {1,2}x{3,4,5} }"? they should then consequently be allowed as subsets of the data domain as well!), but telling my reasons would probably lead to far. However, what is more important, I then do not correctly understand the Direct Semantics: Direct Semantics, 2.2.2: "Data Ranges" <http://www.w3.org/2007/OWL/wiki/Semantics#Data_Ranges> [[ All datatypes in OWL 2 are unary, so each datatype DT is interpreted as a unary relation over ?_D — that is, a set (DT)^DT subset ?_D. Data ranges, however, can be n-ary, as this allows implementations to extend OWL 2 with built-in operations such as comparisons or arithmetic. --> An n-ary data range DR is interpreted as an n-ary relation (DR)^DT over ?_D. ^^^^^^^^ ^^^^ ]] Until now, I have understood the word "over" in the context of the word "relation" to mean (DR)^DT subset (?_D)^n But you seem to suggest that "over" means (DR)^DT subset ?_D without the exponent "n", meaning that dataranges, independent on their arity, are always subsets of the data domain? Since I am an official reviewer of the Direct Semantics, I feel obliged to ask for clarification of the Direct Semantics in this point. Whatever the actual meaning will be in the end, the RDF-Based Semantics will then need to be aligned with the Direct Semantics. Michael >-----Original Message----- >From: Peter F. Patel-Schneider [mailto:pfps@research.bell-labs.com] >Sent: Wednesday, April 01, 2009 11:10 PM >To: Michael Schneider >Cc: public-owl-wg@w3.org >Subject: Re: RDF-Based Semantics and n-ary dataranges > >From: "Michael Schneider" <schneid@fzi.de> >Subject: RE: RDF-Based Semantics and n-ary dataranges >Date: Wed, 1 Apr 2009 21:44:54 +0200 > >>>-----Original Message----- >>>From: public-owl-wg-request@w3.org [mailto:public-owl-wg- >request@w3.org] >>>On Behalf Of Ian Horrocks >>>Sent: Wednesday, April 01, 2009 8:47 PM >>>To: W3C OWL Working Group >>>Subject: RDF-Based Semantics and n-ary dataranges >>> >>>We didn't manage to conclude this discussion. >>> >>>Summary of (my understanding of) the discussion so far: > >[...] > >>>* the structure of n-ary restrictions is defined in SS&FS, but >>>(hopefully) only the unary case can occur in conforming ontologies >>>(as above) >>>* Michael believes that as a result the RDF-Based semantics is broken >> >> Yes, it is _syntactically_ broken. It essentially contains an >expression of >> the form >> >> "<x1,...,xn> in S" >> >> where "S" is defined to denote a subset of the object domain. > >I still don't understand why this can be considered to be syntactically >or semantically or even pragmatically broken. > >It is entirely possible to have an OWL 2 Full interpretation > I = <IR, IP, IEXT, IS, IL, LV> >where LV and thus IR contains not only things like the integers but >also things like pairs, triples, quads, quints, ... over the integers >(or over reals, or over complex numbers, or even over elements in >IR-LV). > >However, even if LV only contains "standard" data values there is >nothing wrong with asking whether LV contains a tuple. This is a >perfectly well-formed question even in this case, it is just that the >answer is then always false. (Which is, of course, the expected and >desirable answer.) > >> If something like this would be written in the Direct Semantics, you >would >> certainly be horrified. > >Why? Again, the answer would just be false. > >> And so you should be for the RDF-Based Semantics as >> well. > >I'm certainly not horrified, and I don't see why anyone would be >horrified. > >> Because this has nothing to do with the distinction between the Direct >> Semantics and the RDF-Based Semantics. It only has to do with what can >be >> written syntactically in the set theory that underlies both our >semantics. > >There is nothing in even set theory that requires that the atomic set >elements not have some internal structure. > >> (There are other problems as well, but I think this is the simplest >one to >> acknowledge.) > >I don't see this problem, nor can I think of any other problems. > >> The problem is: Interpretation function under the semantics of RDF are >> restricted to interpret names by individuals (instances of the domain >IR). >> In addition (in RDFS), there are two functions that allow me to >/indirectly/ >> talk about subsets of the domain IR (the class extension function >> "ICEXT()"), and subsets of the product IRxIR (the property extension >> function "IEXT()"). But there is not yet such a function (or a >collection of >> functions) that allow me to talk about subsets of the products IR^n >for >> arbitrary n. > >I don't follow this reasoning at all. Certainly there is nothing (so >far) that requires tuples to be present in IR, but there is also nothing >(so far) that forbids tuples from being present in IR. > >> So the underlying logic may allow me to write statements as above, at >least >> for an "S" representing a set of n-ary tuples. The problem is that I >do not >> reach this functionality of the underlying logic from within the >current >> framework of the RDFS semantics. So I need to extend this framework. >This is >> what I suggest to do (before April 15th...). > >Again, I don't think that any change is required. As far as I can see, >the RDF-Based Semantics is currently entirely coherent. > >>>* Peter doesn't agree. > >Yep. > >>>Comments? >>> >>>Ian >>> > >> Cheers, >> Michael > >peter -- Dipl.-Inform. Michael Schneider Research Scientist, Dept. Information Process Engineering (IPE) Tel : +49-721-9654-726 Fax : +49-721-9654-727 Email: michael.schneider@fzi.de WWW : http://www.fzi.de/michael.schneider ======================================================================= FZI Forschungszentrum Informatik an der Universität Karlsruhe Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe Tel.: +49-721-9654-0, Fax: +49-721-9654-959 Stiftung des bürgerlichen Rechts, Az 14-0563.1, RP Karlsruhe Vorstand: Prof. Dr.-Ing. Rüdiger Dillmann, Dipl. Wi.-Ing. Michael Flor, Prof. Dr. Dr. h.c. Wolffried Stucky, Prof. Dr. Rudi Studer Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus =======================================================================Received on Friday, 3 April 2009 10:32:14 UTC

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