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Re: [ontolog-forum] Data Models v. Ontologies (again)

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Barker, Sean (UK)" <sean.barker@xxxxxxxxxxxxxx>
Date: Fri, 23 May 2008 10:27:23 +0100
Message-id: <E18F7C3C090D5D40A854F1D080A84CA4F11FB3@xxxxxxxxxxxxxxxxxxxxxx>

This mail is publicly posted to a distribution list as part of a process
of public discussion, any automatically generated statements to the
contrary non-withstanding. It is the opinion of the author, and does not
represent an official company view.    (01)

Thanks to John and all for their comments.     (02)

John Sowa wrote"
I'd replace the phrase "assumes a set of entities" with the 
> phrase "assumes an ontology".  That makes it clear that some 
> kind of ontology is required for data modeling, but it's not 
> the only one."    (03)

Recasting the discussion into pseudo-linear algebra (I'm a mathematician
by trade):    (04)

Databases A, B have data models MA, MB where, say, MA ={e1, e2, e3,...}
for some set of entities ei. The basic data exchange problem is to
construct a transformation T[AB] s.t.    (05)

B' = A.T[AB] + B (B is updated by a translation of the data from A)
    where also MA.T*[AB] = MB (the translation of data is equivalent a
translation of the data model)    (06)

The problem for data exchange is that every transformation T[AB] must be
hand crafted.    (07)

One could rewrite a data model MA in terms of an ontology OA, such that
the ontology OA defined by a basis of ontology classes {o1, o2, o3...}
where every entity in the model has some representation on the ontology
(or at least, every entity in the domain covered by the system, but not
necessarily entities needed for the mechanics of the system).    (08)

The claim for ontologies seems to be that given ontologies OA and OB,
the transformation T[AB]can be <i>automatically</i> constructed.     (09)

The basic problems for ontology are therefore:
- How to define the basis elements oi to enable this to be done;
- How to ensure that the set of basis elements oi are consistent;
- How to ensure that the set of basis elements oi are complete w.r.t.
the domain;
- How to construct an orthogonal basis, such that any data model entity
has a unique representation in oi;
- How to construct the transformations T[AB], ensuring the construction
terminates, or that it terminates within a given time;    (010)

Since in practice, any system is only a partial representation of its
domain, and therefore will be described by a partial ontology, there
exist two further problems:
- How to identify the subsets of OA and OB for which the transformation
can be defined;
- How to identify subsets of OA and OB that in principle cannot be
mapped to each other because of differences in the bases.
(There is also the occasional row over whether it is possible to
construct a single ontology that can form the basis for all domains.)    (011)

In practice, many discussions are framed in terms of particular
representations of an ontology, so two other sorts of problem appear:
- How to create transformations between different representations of an
- How to define a meta-ontology that characterises the representations,
such that the transformations between representations may be constructed
automatically (shades of IDRIS).    (012)

Put in this way, it seems obvious (to me at least) that
        a) Ontology studies in themselves are a sub-branch of
mathematics/logic, being concerned with the properties rather than the
content of an ontology;
        b) The metaphysics which forms the design criteria for the basis
classes (the content) of an ontology is a branch of philosophy;
        c) Knowledge engineering is engineering in so far as it has a
theoretical basis in ontology structure, however much of it is a craft
working in applied metaphysics.
        d) Data modelling is a craft, since it is not based on ontology
studies.    (013)

Conversely, if something is entirely hand crafted so that the structure
cannot be formally analysed, then its a data model, no matter what
language it is written in.    (014)

Sean Barker
BAE SYSTEMS - Advanced Technology Centre
Bristol, UK
+44(0) 117 302 8184    (015)

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Centre, Farnborough, Hants, GU14 6YU, UK
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