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Re: Inferring Class Membership w/o OWL Full?

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 11 May 2004 16:30:35 -0500
Message-Id: <p06001f00bcc6ea6159ba@[10.0.100.76]>
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: Stephen Rhoads <rhoadsnyc@mac.com>, www-rdf-logic@w3.org

>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.

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
>>  >>  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
>>


-- 
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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 17:30:39 UTC

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