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## Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart

 To: "[ontolog-forum] " "AzamatAbdoullaev" Mon, 7 Nov 2011 19:04:38 +0200 <620056FD1CAE4AF6B90A1C954375E4B1@personalpc>
 ```Friday, November 04, 2011 5:47 PM, David Price wrote: "WRT RDF doesn't it simply boil down to being based on graphs which, > quoting from Wikipedia, are "mathematical structures used to model > pairwise relations between objects from a certain collection". So, I'm > confused by comments like "N-ary relations work great in a graph model." > which seems completely at odds with the fact that graph relations are > pairwise."    (01) Indeed. Any graph, as an ordered pair of vertices/nodes/points and edges/links/lines, is a type of binary, two-place or dyadic relation. But an N-relation R is a relation over the sets X1, ., Xn , which is a (n + 1)-tuple R = (X1, ., Xn, G(R)), where G(R) is a subset of the Cartesian product X1 × . × Xn where G(R) is the graph of R. There is also another widespread issue with relations, they are mostly given an extensional interpretation, assuming that the extension of a relation is the relation itself.    (02) Azamat    (03) ----- Original Message ----- From: "David Price" To: "[ontolog-forum]" Sent: Friday, November 04, 2011 5:47 PM Subject: Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart Applications    (04) > WRT RDF doesn't it simply boil down to being based on graphs which, > quoting from Wikipedia, are "mathematical structures used to model > pairwise relations between objects from a certain collection". So, I'm > confused by comments like "N-ary relations work great in a graph model." > which seems completely at odds with the fact that graph relations are > pairwise. > > UML has N-ary associations and AssociationClass, so there's at least one > standard from which the semantics community might steal an idea or two. > > Cheers, > David > > On 11/4/2011 2:57 PM, AzamatAbdoullaev wrote: >> I believe this fundamental issue more belong to the Ontolog Forum. >> Risk to start the n-relations thread... >> >> Azamat >> >> ----- Original Message ----- >> From: "David Booth" >> To: "glenn mcdonald" >> Cc: "AzamatAbdoullaev";; >> "Frank Manola"; "Sampo Syreeni"; >> >> Sent: Friday, November 04, 2011 3:13 PM >> Subject: Standard representations for n-ary relations [was: Re: >> relational >> data as a bona fide member of the SM] >> >> >>> Plus RDF doesn't have any *standard* way to tag or represent n-ary >>> relations -- we have taken a do-it-yourself attitude[1] -- and thus >>> tools cannot predictably recognize n-ary relations as such. >>> >>> Personally, I think this is something that would be good to address, and >>> there are several simple ways it could be done. >>> >>> 1. http://www.w3.org/TR/swbp-n-aryRelations/ >>> >>> David >>> >>> On Fri, 2011-11-04 at 08:49 -0400, glenn mcdonald wrote: >>>> N-ary relations work great in a graph model. The only reason they seem >>>> awkward in the Semantic Web world, in my opinion, is that RDF leads us >>>> to looking at a graph *decomposition* instead of an actual assembled >>>> graph. This effect cascades onto SPARQL and OWL, and thus we end up >>>> with a great forest we're reduced to looking at, and talking about, >>>> one twig at a time. >>>> >>>> glenn >>>> >>>> >>>> On Friday, November 4, 2011, AzamatAbdoullaev >>>> wrote: >>>>> That's a big issue of Relational Ontology, or "N-Relational Ontology >>>> of Things", as discussed 5 years ago: >>>>> http://lists.w3.org/Archives/Public/semantic-web/2006Apr/0047.html. >>>>> And it is not strange that a consistent formal account of >>>> N-Relations has been long missing. Relations are so ubiquitious and >>>> omnipresent that most people take them for granted. In a general >>>> sense, everything is related to everything. We are related to the >>>> world around us, to other people, to our country, to our family and >>>> children and to ourselves. There are ontological, logical, natural, >>>> physical, mechanical, biological, psychological, >>>> emotional, technological, social, cultural, moral, sexual, aesthetic, >>>> and semiotic relations, to name a few. For most people, there is no >>>> particular problem with most of these relations, may be, except >>>> ontological and semiotic (semantic, syntactic and pragmatic) >>>> relations. However, theorists have been perpetually puzzled over >>>> relations, and they have tried to understand them theoretically and >>>> systematically, but consistent, machine-readable models of relations >>>> have proved extraordinarily difficult to construct: >>>>> "What Organizes the World: N-Relational Entities": >>>> >http://www.igi-global.com/chapter/reality-universal-ontology-knowledge-systems/28313 >>>>> What is hardly questionable, to be implemented, the semantic web >>>> indeed requires a unified formal ontology of relations: UFOR. >>>>> Azamat Abdoullaev >>>>> >>>>> ----- Original Message ----- >>>>> From: Frank Manola >>>>> To: Alexandre Riazanov >>>>> Cc: Semantic Web List >>>>> Sent: Friday, November 04, 2011 1:23 AM >>>>> Subject: Re: relational data as a bona fide member of the SM >>>>> >>>>> On Nov 3, 2011, at 6:22 PM, Alexandre Riazanov wrote: >>>>> >>>>> >>>>> On Thu, Nov 3, 2011 at 5:20 PM, Frank Manola >>>> wrote: >>>>> On Nov 3, 2011, at 3:19 PM, Alexandre Riazanov wrote: >>>>> >>>>> I have been asking this sort of questions for a while and the only >>>> decent answer I know is that >>>>> Description Logics only work with unary and binary predicates >>>> (classes and properties), >>>>> although I believe RDF was initially developed independently from >>>> the DL and OWL work. >>>>> RIF and RuleML seem to be going in the relational direction (see >>>> also the earlier work >>>> >http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.48.7623&rep=rep1&type=pdf >>>> by Harold Boley), but it is difficult to break the monopoly >>>>> of RDF+OWL. >>>>> >>>>> From my point of view, a major reason for focusing on unary and >>>> binary predicates (the logical forms that underlie RDF triples) is >>>> that it's easier to deal with the problems of integrating >>>> heterogeneous data (a key issue in the semantic web) if the data is in >>>> (or is mapped to being in) that form, as opposed to data in arbitrary >>>> arity relations (for example, with n-aries you need a schema to >>>> interpret any tuples you encounter "in the wild", otherwise you don't >>>> know what the "columns" mean). If you go back to the period before >>>> the "monopoly of RDF+OWL" :-) and look at the work on integrating >>>> heterogeneous relational databases, one of the major approaches to >>>> developing the mappings between the various relational schemas was by >>>> interpreting the various local schemas in terms of unary and binary >>>> relations for just this reason (compound keys had to be dealt with in >>>> this way too, because the same combinations of columns didn't >>>> necessarily constitute the keys in otherwise corresponding relations >>>> in the different local schemas). Mind you, if you're NOT worried >>>> about integrating heterogeneous data, RDF introduces extra pain of its >>>> own (figuring out all those identifiers, for one thing), but if you >>>> ARE worried about integrating heterogenous data, I think you want >>>> those identifiers around. >>>>> I don't quite understand your argument. Indeed, interoperability is >>>> the target. Syntactic interoperability is not a problem as long as you >>>> use the same or convertible syntaxes. >>>>> Semantic interoperability requires shared understanding of the >>>> identifiers being used, which has nothing to do with arity. >>>> Reinterpreting legacy relational schemas is a related, but separate >>>> issue. >>>>> Binary predicates are often handy to represent attributes, but it >>>> does not mean n-ary predicates cannot be helpful in the same (although >>>> I could not recall a real example) and other KR tasks. >>>>> Let me try again, then (although I can't guarantee I'll be any more >>>> understandable this time!). The original question (I thought) was why >>>> there weren't relational approaches applied in Semantic-Web-like >>>> contexts (where, as you say, interoperability is the target). I cited >>>> the integration of heterogeneous relational databases to argue that, >>>> in this case, where relations were already being used by all parties, >>>> and interoperability was the target, those doing the integration found >>>> that using unaries and binaries helped (I agree that shared >>>> understanding of the identifiers is necessarily for semantic >>>> interoperability, but in RDF+OWL, at least the identifiers are >>>> *there*; those putting the data on the Web had to create them). All >>>> that RDF is doing is starting from the unaries and binaries. This is >>>> not an argument that n-ary relations aren't helpful in data modeling. >>>> Nor is it an argument that you can't do semantic integration using >>>> n-ary relations. I simply think it's *easier* to do that integration >>>> with the RDF approach, and I cited an historical example as evidence >>>> that others have found that as well. Now, they/we may have simply >>>> missed the boat, and if so, someone (possibly you) will have to come >>>> along and show us a better way (I'm serious). There have certainly >>>> been attempts to provide more general KRs (allowing n-ary predicates) >>>> for data/knowledge exchange >>> -- >>> David Booth, Ph.D. >>> http://dbooth.org/ >>> >>> Opinions expressed herein are those of the author and do not necessarily >>> reflect those of his employer. >>> >>> >> >> _________________________________________________________________ >> 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 >> >> > > > -- > Managing Director and Consultant > TopQuadrant Limited. Registered in England No. 05614307 > UK +44 7788 561308 > US +1 336-283-0606 > > > > > _________________________________________________________________ > 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 >    (05) _________________________________________________________________ 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    (06) ```
 Current Thread Re: [ontolog-forum] Self Interest Ontology, (continued) Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart Applications, AzamatAbdoullaev <= Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart Applications, Duane Nickull