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Re: Inferring Class Membership w/o OWL Full?

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Wed, 12 May 2004 01:08:36 +0100
Message-ID: <16545.27396.999588.637867@excalibur.cs.man.ac.uk>
To: Pat Hayes <phayes@ihmc.us>
Cc: Stephen Rhoads <rhoadsnyc@mac.com>, www-rdf-logic@w3.org

On May 11, Pat Hayes writes:
> 
> >On May 7, Pat Hayes writes:
> >>
> >>  >For those who didn't follow the debates on the webont mailing list, I
> >>  >should perhaps draw your attention to the sad history of Pat's morbid
> >>  >obsession with DLs. I had hoped that having recognised the problem [1]
> >>  >(the first and hardest step) he would by now be well on the road to
> >>  >recovery. Sadly, it would appear that this is not the case. In fact
> >>  >this is not Pat's first relapse [2], so perhaps we shouldn't be
> >>  >surprised.
> >>  >
> >>  >Ian
> >>  >
> >>  >[1] http://lists.w3.org/Archives/Public/www-webont-wg/2002Sep/0411.html
> >>  >[2] http://lists.w3.org/Archives/Public/www-webont-wg/2002Dec/0092.html
> >>
> >>  Perhaps also not uncharacteristically, Ian manages to simultaneously
> >>  be insulting, offensively ad-hominem and to mislead the unwary
> >>  reader.  The acknowledgement in [1] was to a completely unrelated
> >>  misunderstanding arising in part from my reaction to an extended
> >>  series of memoranda claiming to show that (what is now called)
> >>  OWL-Full was impossible, by a specious reference to the set-theoretic
> >>  paradoxes, but also in part, I concede, from my own ignorance of DL
> >>  metatheory at that time. The opinions I expressed in [2] are
> >>  unrelated to [1] , are not a 'relapse' - to acknowledge that DLs are
> >>  a subset of FOL is not to endorse the basing of the entire SW effort
> >>  on that subset - and I still hold them, and will continue to hold
> >>  them.
> >>
> >>  I won't react to such jibes in future, but the record should be 
> >>set straight.
> >
> >Strangely enough, that is exactly what I told myself when I read your
> >initial email.
> >
> >The point I was trying to make with my [witty banter|vile character
> >assassination]* is that, amusing though your ritual DL bashing is, it
> >obscures the fact that the restriction being discussed here, i.e., not
> >being able to create a subPropertyOf rdf:type, is nothing to do with
> >DLs per se, but is required in order to keep the language inside what
> >I think we agreed to call "conventional" FOL.
> 
> I disagree. rdf:type is simply a binary relation. It happens to be 
> related to the operation of unary predication in a systematic way, 
> which can be expressed in SCL-FOL (though not using a syntax that you 
> would honor with the term 'conventional') by the axiom
> 
> (iff (rdf:type x y)  (y x) )
> 
> and in a more conventional syntax by the axiom
> 
> (rdf:type x y) iff (holds y x)
> 
> but the special nature of this axiom does not affect the fact that 
> rdf:type is a binary relation. To amplify the point, the operation of 
> creating a subproperty of rdf:type is quite meaningful and has some 
> obvious first-order consequences, such as (using SCL notation and 
> omitting universal quantifiers)
> 
> (iff (rdf:type x y)  (y x) )  ...1 (RDF axiom)
> (subProperty foo rdf:type)  ...2
> (implies (subProperty x y) (implies (x z u) (y z u)))  ....3 (RDFS axiom)
> (foo thing class)  ...4
> |=
> (class thing)
> 
> proof:
> (implies (foo z u) (rdf:type z u) )  ....5 (3, UInstance; 2, Modus Ponens)
> (rdf:type thing class)  ...6 (5, Uinstance; 4, Modus Ponens)
> (class thing)  (1, conj; Uinstance; 6, Modus Ponens)
> 
> Or you could derive it by unit resolution once the implications and 
> iff were translated into clauses in the usual way. The only thing 
> unconventional about this is that it systematically suppresses the 
> 'holds' relation by allowing variables to occur in predicate 
> position, which does not significantly affect any of the FO 
> metatheory.

I am aware of the conjecture that there is a satisfiability preserving
transformation from an OWL-Full ontology into a "conventional" FOL
theory. I have yet to see any proof of the correctness of this
transformation.

Ian


> My 'DL police' [witty banter|vile character assassination]* was a 
> reference to the fact that OWL-DL (hence the "DL") has been 
> thoroughly checked and constrained so as to not permit a range of 
> modes of expression, and that if something appears to be 
> syntactically illegal by virtue of these rules, the chances of one 
> being able to wriggle past the constraints by some superficial 
> transformations, as Stephen had suggested, are vanishingly low. This 
> remark was in part a testament to the thoroughness of the job done by 
> you and Peter in defining the OWL-DL syntactic conditions, in fact. 
> As you point out, not all these restrictions arise from the need for 
> OWL-DL to be a description logic. Nevertheless, for whatever reason, 
> they have been imposed on the language, and I do not think it is 
> misleading to imply that they were imposed largely at the behest of 
> those who were most enthusiastic about DLs.
> 
> >In fact separating the
> >syntax of the language from the domain of discourse is fundamental to
> >most logics.
> 
> I agree; however, this has nothing to do with the topic. The point is 
> that there can be systematic alternative representations of the same 
> fact within a single syntax. This is an elementary truism about 
> logics of any reasonable expressivity, and is one of the reasons we 
> have notions like "normal form".
> 
> Pat
> 
> >
> >Ian
> >
> >* delete as appropriate
> >
> >
> >
> >>
> >>  Pat
> >>
> >>  >
> >>  >On May 7, Pat Hayes writes:
> >>  >>
> >>  >>  >I realize that everyone is probably beat from that "Classes as
> >>  >>  >Values" discussion in the SWBP, but ... no thoughts on this?
> >>  >>  >
> >>  >>  >Would it be unthinkable to create a subPropertyOf rdf:type?
> >>  >>
> >>  >>  Its explicitly forbidden in OWL-DL by edict of the DL police, but it
> >>  >>  makes perfect semantic sense and could be done in OWL-Full. On the
> >>  >>  other hand, why not just use rdf:type? What do you gain from the
> >>  >>  explicit subpropertying?
> >>  >>
> >>  >>  If you thought to sneak past the DL syntax restrictions, forget it.
> >>  >>  The DL police have already thought of all the tricks you could use
> >>  >>  and blocked all the exits.
> >>  >>
> >>  >>  Pat
> >>  >>
> >>  >>  >Something like ...
> >>  >>  >
> >>  >>  ><owl:ObjectProperty rdf:ID="hasGenre">
> >>  >>  >    <rdfs:subPropertyOf rdf:resource="&rdf;type"/>
> >>  >>  ></owl:ObjectProperty>
> >>  >>  >
> >>  >>  ><ex:Song rdf:ID="PurpleHaze">
> >>  >>  >    <ex:hasGenre rdf:resource="&ex;ClassRockMusic"/>
> >>  >>  ></ex:Song>
> >>  >>  >
> >>  >>  >Thus, the Individual "PurpleHaze" is an instance of both Song and
> >>  >>  >ClassicRockMusic.
> >>  >>  >
> >>  >>  >Note that the intent is state class membership, not to say that the
> >>  >>  >"subject" of the Song is a concept denoted by a Class (as in the
> >>  >>  >"Classes as Values" paper).
> >>  >>  >
> >>  >>  >--- Stephen
> >>  >>  >
> >>  >>  >
> >>  >>  >On Apr 24, 2004, at 4:50 PM, Stephen Rhoads wrote:
> >>  >>  >
> >>  >>  >>
> >>  >>  >>Folks,
> >>  >>  >>
> >>  >>  >>There are various parts of my (Media Publishing and Distribtuion)
> >>  >>  >>ontology where I would like to avoid the requirement of "multiple
> >>  >>  >>typing".  The objective here is to simplify the ontology and user
> >>  >>  >>interfaces which employ it.
> >>  >>  >>
> >>  >>  >>A user of the ontology should be able to simply declare an
> >>  >>  >>Individual to be a Song, Album, Movie, MovieSeries,
> >>  >>  >>TelevisionProgram, TelevisionSeries, RadioProgram or RadioSeries.
> >>  >>  >>Other important class membership should be inferred by property
> >>  >>  >>values.  A TelevisionSeries, for example, could have
> >>  >>  >>"hasSeriesType" of "SeasonalSeries" and thus be a member of that
> >>  >>  >>Class.  A Movie could have "hasGenre" of "Drama" and thus be a
> >>  >>  >>Drama.
> >>  >>  >>
> >>  >>  >>The problem is that I can't see how to model this without landing
> >>  >>  >>in OWL Full.  Take the following example:
> >>  >>  >>
> >>  >>  >>A sample Class hierarchy:
> >>  >>  >>
> >>  >>  >>Music
> >>  >>  >>    ElectronicMusic
> >>  >>  >>    PopMusic
> >>  >>  >>    RockMusic
> >>  >>  >>       ClassicRockMusic
> >>  >>  >>       GlamRockMusic
> >>  >>  >>       GrungeRockMusic
> >>  >>  >>
> >>  >>  >>And sample Class description:
> >>  >>  >>
> >>  >>  >><owl:Class rdf:ID="ClassicRockMusic">
> >>  >>  >>    <rdfs:subClassOf rdf:resource="#RockMusic"/>
> >>  >>  >>    <owl:equivalentClass>
> >>  >>  >>       <owl:Restriction>
> >>  >>  >>          <owl:onProperty rdf:resource="#hasGenre"/>
> >>  >  > >>          <owl:hasValue rdf:resource="#ClassicRockMusic"/>
> >>  >>  >>       </owl:Restriction>
> >>  >>  >>    </owl:equivalentClass>
> >>  >>  >></owl:Class>
> >>  >>  >>
> >>  >>  >>In other words, if the Individual (a Song or Album) hasGenre
> >>  >>  >>ClassicRockMusic, then it *is* ClassicRockMusic (or at least a
> >>  >>  >>member of a Restriction Class with the same class extension).  But
> >>  >>  >>(I think) this puts the ontology into OWL Full because
> >>  >>  >>ClassicRockMusic is being treated as both a Class and an Individual
> >>  >>  >>(I can confirm that Racer will not accept the ontology from Protege
> >>  >>  >>because it is "not in OWL DL").
> >>  >>  >>
> >>  >>  >>Thoughts?  Solutions?
> >>  >>  >>
> >>  >>  >>--- Stephen
> >>  >>
> >>  >>
> >>  >>  --
> >>  >>  ---------------------------------------------------------------------
> >  > >>  IHMC	(850)434 8903 or (650)494 3973   home
> >>  >>  40 South Alcaniz St.	(850)202 4416   office
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> >>  >>  FL 32501			(850)291 0667    cell
> >>  >>  phayes@ihmc.us       http://www.ihmc.us/users/phayes
> >>  >>
> >>
> >>
> >>  --
> >>  ---------------------------------------------------------------------
> >>  IHMC	(850)434 8903 or (650)494 3973   home
> >>  40 South Alcaniz St.	(850)202 4416   office
> >>  Pensacola			(850)202 4440   fax
> >>  FL 32501			(850)291 0667    cell
> >>  phayes@ihmc.us       http://www.ihmc.us/users/phayes
> >>
> 
> 
> -- 
> ---------------------------------------------------------------------
> IHMC	(850)434 8903 or (650)494 3973   home
> 40 South Alcaniz St.	(850)202 4416   office
> Pensacola			(850)202 4440   fax
> FL 32501			(850)291 0667    cell
> phayes@ihmc.us       http://www.ihmc.us/users/phayes
> 
Received on Tuesday, 11 May 2004 18:08:25 UTC

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