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Re: The notion of a "classification criterion" as a class

From: Pat Hayes <phayes@ihmc.us>
Date: Fri, 30 Apr 2010 13:58:01 -0500
Cc: "[ontolog-forum]" <ontolog-forum@ontolog.cim3.net>, public-owl-dev <public-owl-dev@w3.org>, rector@cs.man.ac.uk, sowa@bestweb.net
Message-Id: <AA2CE508-26EA-4E2E-9274-4369C7B1FA68@ihmc.us>
To: Bene Rodriguez-Castro <beroca@gmail.com>

On Apr 30, 2010, at 7:22 AM, Bene Rodriguez-Castro wrote:

> On Sun, Apr 25, 2010 at 8:56 AM, Pat Hayes <phayes@ihmc.us> wrote:
>>
>> But why would it be hard to accept? After all, the semantic model
>> underlying OWL-DL is very straightforward. So, ask how your vision  
>> can
>> be re-stated in terms of classes considered as simple sets. What
>> differences **between sets** could account for the distinction  
>> between
>> Wines and WinesByColor ? And I think it is fairly clear that there is
>> no difference between them, when they are considered as sets,
>> independent of the class hierarchy you see them as belonging in. They
>> have to be the same set: so, in OWL-DL, they have to be the same  
>> class.
>>
>> I suspect that you are used to thinking of classes as nodes in a
>> classification hierarchy, but that is not the primary OWL intuition.
>> The subclass hierarchy in OWL-DL is simply a consequence of the
>> extensional subset relationship: if all the members of A are also
>> members of B, then A is a subClass of B. That is what subClass
>> **means** in OWL-DL (and similar languages.)
>>
>> I find it interesting that you feel that the normalized ontology  
>> seems
>> to 'need' these XByY classes, and that the **structure** 'seems to be
>> asking' for them (my emphasis.) But this way of thinking is entirely
>> alien to the semantics of OWL (or any other extensional - set-based -
>> language), where the 'structure' of the subsumption hierarchy is
>> emergent rather than imposed from above. Subsumption here is a binary
>> relation between sets, and is determined entirely by their  
>> membership.
>> Any "structure" that the overall hierarchy has must arise from this
>> purely binary relationship.
>>
>> Good luck with your project, but you need to be using a formalism  
>> with
>> a different kind of underlying semantics than that used by OWL-DL.
>>
>> Pat Hayes
>>
>
> Hi Pat,
>
> I can see now that under OWL semantics it is not useful to introduce
> these XbyY classes in the inheritance structure of the ontology.
> However, I might still have to find a sensible mechanism to represent
> in OWL DL the type of information that these classes provide.  I'll
> try to summarize the main reasons for this in my research because it
> is very possible that some of the assumptions along the way are
> debatable.
>
> * The aim is to put forward an ontology design pattern (or patterns)
> within OWL DL to model a particular type of domain concept.  A domain
> concept prone to be represented by multiple alternative classification
> criteria (similar to the examples of :Person, :Wine or to an
> additional example cited below, "dish detergent").
>
> * After a survey of ontology design methodologies, there seems to be a
> lack of guidelines on how to *identify* the classification criteria of
> such concepts and how these concepts can be represented *together with
> their classification criteria* in an ontology model.
>
> * To *identify* the relevant classification criteria to be considered,
> I am trying to propose an adaptation of part of Spiteri's simplified
> model for *facet analysis*[1][5].

Good call, to refer me to my own comment :-)

> As a neat example, notice the
> conceptualization of the "dish detergent" concept developed using
> Spiteri's method in this technical report[2].

There is a revealing passage in there:
"...facets are a natural way of organizing things. Many web designers  
have probably rediscovered them independently by asking, "What other  
ways would people want to view this data? What's another way to slice  
it?""

And it seems to me, you see, that this is exactly what an *ontology*  
should NOT seek to do. The basic underlying idea of ontology  
engineering is that the 'way of viewing' should emerge from the  
assumptions made about what things are there, not be imposed from  
outside by a 'classification scheme'. I think it is significant that  
this whole topic emerges from library science rather than from the  
philosophical traditions of ontology or metaphysics.

>  I think the final
> conceptualization obtained in the form of a "faceted classification
> scheme", could be a suitable starting point for the representation of
> (in this case) the "dish detergent" domain concept in an ontology
> model where (in most cases), a facet would correspond to a
> classification criterion.  (Incidentally, some comments in this
> ontolog-forum thread[3][4][5] speaks favorably of the use of faceted
> classification systems as a point of reference for ontology design).

Right. I am myself less sanguine that others about their utility for  
ontology work, but let us not quibble.

>
> * To provide a "valid" fit-for-purpose OWL DL representation of this
> particular type of domain concept, I intend to use the cited
> Normalisation mechanism which seems a very suitable and effective
> approach to achieve it.  The mechanism refers to different "semantic
> axes" of the domain concept being normalised where (in most cases) a
> semantic axis would correspond to a classification criterion.
> (Nonetheless, as per John's recommendation, I will look into FCA
> methods as well).

Well, OK. It seems to me that the kind of structure described in [2]  
are most accurately defined in OWL by using classes of classes (or, to  
pull this all back into OWL-DL, classes of individuals which encode  
class categories: see below for details.) Thus, [2] says " ... a  
faceted classification [is] a set of mutually exclusive and jointly  
exhaustive categories...". That is straightforward: each facet is a  
set of subsets of the main category which are exhaustive and mutually  
exclusive; in set-theory language, a cover. That would be a class of  
classes in OWL, which takes us outside the DL fragment, but we can get  
back into it by treating them as individuals which are values of a  
property corresponding the facet. So for example the color facet of  
wine would be the property hasColor, with the values {red, white,  
rose} and the various OWL-defined restriction classes would be  
mutually disjoint, which follows in fact from the distinctness of the  
values. So, the facet corresponds to the particular property, and we  
could express this by asserting that the is a 'facet' property for the  
main class:  ex:Wines :hasFacet ex:hasColor . Now, this of course does  
not fit into OWL-DL (sigh), but I believe it could be handled in OWL2,  
using the 'punning' device that allows properties and classes to be  
treated as individuals. And of course it is fine in OWL-Full or common  
logic.

>
> * But in addition, I would propose to "augment" the normalised
> ontology model to include information about how many classification
> criteria of the domain concept in question are represented in the
> model and which classes (or properties) are associated to each
> classification criterion.  This is the idea that motivated the "need"
> of the hypothetical XbyY classes.
>
> * After comments in this thread, I believe the information provided by
> the XbyY classes could be considered "meta-knowledge" (knowledge about
> elements of the ontology, in this case other classes).

More accurately described as 'higher-level' knowledge, but  
unfortunately the incorrect "meta-" usage has become too common to  
eliminate. (All knowledge in an ontology is 'knowledge about elements  
of the ontology'.)

>  The potential
> representation of this meta-knowledge about classification criteria,
> could effectively provide a "mapping" between the ontology and the
> faceted classification scheme that the ontology was based on.
> "Faceted-friendly" applications aware of this mapping, could exploit
> it for example, enabling new ways of visualizing, navigating or using
> the data that will populate the ontology over time.

True.

Good luck with your project.

Pat Hayes

>
> This overall overview summarizes the main "dots I'm trying to connect"
> throughout this research and I guess a rather long answer to why I
> thought the normalized ontology "needed" these XbyY classes.
>
> Lastly, two preliminary ideas in a very early stage, that I gathered
> and that I am exploring to capture this classification criteria
> meta-knowledge:
>
> * Specialization of OWL Annotation properties given that at the moment
> I don't see the need to reason over this type of information.
>
> * A separate RDF or OWL vocabulary to be defined for my purpose,
> similar to the OMV (Ontology Metadata Vocabulary) approach[6].
>
> As always, thanks indeed for any comments you or fellow readers may  
> have!
>
> Regards,
> Bene
>
> ----
> [1] Spiteri, 1998. A Simplified Model for Facet Analysis.
> http://iainstitute.org/en/learn/research/a_simplified_model_for_facet_analysis.php
>
> [2] Denton, 2003. How to Make a Faceted Classification and Put It On  
> the Web.
> http://www.miskatonic.org/library/facet-web-howto.html
>
> [3] John F. Sowa, 2008/06/22:
> http://ontolog.cim3.net/forum/ontolog-forum/2008-06/msg00028.html
> [4] John F. Sowa, 2008/06/22:
> http://ontolog.cim3.net/forum/ontolog-forum/2008-06/msg00034.html
> [5] Pat Hayes, 2008/06/23:
> http://ontolog.cim3.net/forum/ontolog-forum/2008-06/msg00040.html
>
> [6] Hartman et al., 2005. Ontology Metadata Vocabulary and
> Applications. OTM Workshops 2005: 906-915.
>

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Received on Friday, 30 April 2010 18:59:11 GMT

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