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

 To: "[ontolog-forum] " David Leal Thu, 11 Mar 2010 09:26:16 +0000 <1.5.4.32.20100311092616.020dfda0@xxxxxxxxxxxxxxxx>
 ```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. > > > 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" 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 registered in England no. 2422371 tel: +44 (0)20 8857 1095 mob: +44 (0)77 0702 6926 e-mail: david.leal@xxxxxxxxxxxxxxxxxxx web site: http://www.caesarsystems.co.uk ============================================================    (09) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (010) ```
 Current Thread Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping, (continued) Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping, David Leal <= Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping, sowa Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping, Matthew West