Dear Sean and Pat, (01)
A possible approach to 2D and 3D points is as follows: (02)
Dimensionality is defined for topological structures. A topological
structure is a set of things, with a set of subsets that express closeness
between members of the set. A topological structure can be a 1D manifold, a
2D manifold, etc.. (03)
A thing within a topological structure is refered to as a "point". Where the
chosen topological structure is a 2D manifold, we can refer to the thing as
a "2D point". Probably the term "2D point" refers to a (thing, 2D manifold)
pair. A thing can be part of more than one topological structure, so there
may also be a (thing, 3D manifold) pair for the same thing. (04)
A similar situation occurs with the term "vertex" in a graph (which consists
of vertices and edges). Probably the term vertex refers to a (thing, graph)
pair, where the thing plays the role of a vertex in the graph. In a
different graph, the same thing could be a subgraph. (05)
EXAMPLE: Oxford Circus is a vertex in the London Undergound route graph.
When you are there it seems to have a lot of internal structure, with many
entrances and exits. (06)
Best regards,
David (07)
At 14:49 10/03/2010 -0500, you wrote:
>
>Sean,
>
> 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?
>
>
>
>Pat
>
>
>
>Patrick Cassidy
>
>MICRA, Inc.
>
>908-561-3416
>
>cell: 908-565-4053
>
>cassidy@xxxxxxxxx
>
>
>
>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
>
>
>
>
>
>
>
>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.
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> 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 (08)
============================================================
David Leal
CAESAR Systems Limited
registered office: 29 Somertrees Avenue, Lee, London SE12 0BS
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tel: +44 (0)20 8857 1095
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e-mail: david.leal@xxxxxxxxxxxxxxxxxxx
web site: http://www.caesarsystems.co.uk
============================================================ (09)
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