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

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Patrick Cassidy" <pat@xxxxxxxxx>
Date: Wed, 10 Mar 2010 14:49:47 -0500
Message-id: <0b3301cac08a$d7390aa0$85ab1fe0$@com>


   I could use some clarification:

[SB] > 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.


I have been assuming that a point has zero dimensions, and can exist in any coordinate system of any dimensionality.  There is an issue as to whether, for example, a 1D line of zero length is identical to a point.  That may require a translation.  What have I missed?




Patrick Cassidy



cell: 908-565-4053



From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of sean barker
Sent: Wednesday, March 10, 2010 2:34 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping






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

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

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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.


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
   Aykut Firat, Information Integration Using Contextual Knowledge and Ontology Merging. MIT (Sloan School of Management) Ph. D thesis, September 2003.
   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

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