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Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Kevin D Keck <KDKeck@xxxxxxx>
Date: Fri, 26 Mar 2010 17:43:25 -0700
Message-id: <f18019074497.4bacf23d@xxxxxxx>
I believe the variety of reification you use as an example (cartesian vs. polar 
coordinates) is exactly what is addressed in OWL2 by hasKey axioms:    (01)

R2Point a owl:Class ;
  owl:hasKey ( x y ) ;
  owl:hasKey ( r theta ) .    (02)

The formal semantics of OWL2 restricts the applicability of such axioms to 
named individuals out of concerns about tractability, but this technical issue 
can at least be worked around, if not someday soon happily resolved.    (03)

Another variety is addressed by property chains.  Consider a property o1:stole 
which is elsewhere "reified" as a class o2:Theft with properties (presumably 
among others) o2:thief and o2:article; a mapping between them could be asserted 
as:    (04)

o1:stole owl:equivalentProperty [owl:propertyChainAxiom (
  [owl:inverseOf o2:thief]
  o2:article ) ] .    (05)

It may be more complicated than this in general, but I think property chains 
are adequate to address this general variety of reification.    (06)

Is there another variety of reification which is not addressed by OWL2?    (07)

----- Original Message -----
From: sean barker <sean.barker@xxxxxxxxxxxxx>
Date: Wednesday, March 10, 2010 11:35 am
Subject: Re: [ontolog-forum] Re  Foundation ontology, CYC, and Mapping
To: ontolog-forum@xxxxxxxxxxxxxxxx    (08)

> Re: [ontolog-forum] Re  Foundation ontology, CYC, and Mapping
> Duane
> Chris Menzel was right in saying it's not that subtle. The term 
> type here refers to the abstract data type used to reify the 
> concept - for example, does one reify a latitude as a real number, 
> a fixed precision decimal number, or as a triple of integers for  
> degree, minute, second. 
> This is distinct from the problem 3D v 4Dism that Matthew referred to.
> One of the problems I have not seen discussed much - possibly 
> because I have been looking in the wrong place - is the relation in 
> ontology languages between concepts and their reification, as 
> opposed to the relation between different concepts. For example, I 
> would regard 2D and 3D points as referring to different concepts, 
> whereas Cartesian co-ordinate systems v. polar co-ordinate systems 
> for a 2D point as different reifications of the same concept. 
> Looking at languages like OWL, it seems that the reification is 
> identified with form of the concept, as if there is only one way of 
> reifying it.
> Having two different reifications of a concept should not be a 
> major semantic challenge, the challenge is that, unless you account 
> for the different reifications, the systems cannot interoperate. 
> However there may be practical problems concerning the adequacy of 
> the reifications. See, for example, Cliff B Jones, "Systematic 
> Software Development using VDM", Chapter 8 on Data reification for 
> a more detailed treatment.
> The converse is what John Sowa keeps insisting on, that 
> interoperation happens mostly at the level of middle ontologies. In 
> this case, there is some morphism between the reifications - or at 
> least a subset of the reifications - which can be used for 
> interoperation. For example, there is a simple morphism between 
> points in Euclidean space and those in a homogenious co-ordinate 
> system. In one dimension this is
>    E(x) -> H(x, 1) and H(x, 1) -> E(x).
> This breaks down for points of the form H(x, 0), but then 
> Eucllidean spaces doesn't have a lot to say about points at infinity.
> Sean Barker
> Bristol
> --------------------------------------------------------------------
> ------------
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Duane Nickull
> Sent: 09 March 2010 22:41
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping
>                    *** WARNING ***  This message has originated 
> outside your organisation,  either from an external partner or the 
> Global Internet.       Keep this in mind if you answer this 
> message.Sean:
> For the second of these (conflicts when the same concept is 
> represented by different types), can you elaborate a couple of 
> examples (no hurry).  I just want to make sure I have a good idea 
> of this. 
> Duane
> On 3/9/10 2:30 PM, "sean barker" <sean.barker@xxxxxxxxxxxxx> wrote:
>  Apologies for slow response to a couple of requests for sources 
> on semantic incompatibilities.
>  This is the table we generated internally, based partly on older 
> database work
>    Semantic Incompatibilities 
>    Naming  Conflicts  When objects  representing the same concept 
> may contain dissimilar names: conflicts due  to either homonyms or 
> synonyms. 
>    Type  Conflicts  When the same  concept is represented by 
> different types. 
>    Key  Conflicts  When different  keys are assigned to the same 
> concept in different schema.   
>    Behavioural  Conflicts  When different  insertion/deletion 
> policies are associated with the same class of objects  in 
> different schemata. e.g. deleting an object may leave an "empty" 
> object  rather than a "null reference". 
>    Missing  Data  When different  attributes are defined for the 
> same concept. 
>    Levels of  Abstraction  When  information about an entity is 
> stored at dissimilar levels of detail. e.g.  'name' versus 
> 'first_name' and 'last_name'. 
>    Identification of  Related Concepts  For example,  two entities 
> belonging to two different databases may not be equivalent  but one 
> entity may be a generalisation of the other  entity. 
>    Scaling  Conflicts  When the same  attribute of an entity is 
> stored in dissimilar  units.
>  it is based on/taken from
>  [1]    Aykut Firat, Information Integration Using Contextual 
> Knowledge and Ontology Merging. MIT (Sloan School of Management) 
> Ph. D thesis, September 2003.
>  [1]    M. P. Reddy, B. E. Prasad, P. G. Reddy, Amar Gupta, A 
> Methodology for Integration of Heterogeneous Databases, IEEE 
> Transactions on Knowledge and Data Engineering, Vol. 6, No. 6, 
> December 1994.
>  There are some other papers dating from the mid-nineties, but 
> they have not survived my various office moves. 
>  Sean Barker
>  Bristol
>     (09)

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