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

 To: , "[ontolog-forum] " "AzamatAbdoullaev" Mon, 7 Nov 2011 23:54:00 +0200 <54E914AD589C47CCB7D313B368CE6DDD@personalpc>
 ``` ----- Original Message ----- From: "doug foxvog" To: "[ontolog-forum]" Sent: Monday, November 07, 2011 9:24 PM Subject: Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart Applications    (01) On Mon, November 7, 2011 12:04, AzamatAbdoullaev said: > 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."    (02) > 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.    (03) While N-ary relations are not best suited to expression in a graph model, they can be so expressed. Each statement expressed by an N-ary relation is modeled as a node, with a typed link (relation) for each of the N arguments. This ends up being a reification of the assertion.    (04) AA: Not quite clear: if you are talking about pseudograph, or multigraph, permitting multiple edges, defining the edges as the first-class entities as nodes, having its own identity, and so including the so-called provenance information, also adding dimensions.    (05) If several arguments of the N-ary relation are interchangable, then the same relation is used from the reified assertion to each of those arguments. In this way, multiple N-ary assertions which express the same meaning are mapped to the same reified assertion.    (06) E.g., (isBetween X Y Z) might be equivalent to (isBetween X Z Y), but both would map to an IsBetweenAssertion node with (initially) three associated links: (boundaryIBA IBA12345 Y) (boundaryIBA IBA12345 Z) (betweenIBA IBA12345 X) More assertions could be made about this reified assertion: (holdsDuring IBA12345 ReifiedTimePeriod2103470734) (reliability IBA12345 FairReliability) (assertedBy IBA12345 DougFoxvog) (betweennessType IBA12345 SpatialBetweenness)    (07) > 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.    (08) By whom is this interpretation "mostly" given? AA: In formal logic, as Chris mentioned. Besides, in graph theory, defining lines/edges as pairs of nodes or vertices, you "extending" a relationship. In mathematics, the extension of a set is the set itself, a function is extended by a set of ordered pairs (arguments and values). In computer science, the extension of data bases, the particular instances, while the schema/model/structure is its intension, and so on. As you know, definition by genus and difference falls into an intensional description, as well as axioms, laws and rules and principles. Azamat -- doug f    (09) > Azamat > > > > ----- 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 > > >> 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 >> > > > _________________________________________________________________ > 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 > >    (010) ============================================================= doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org    (011) "I speak as an American to the leaders of my own nation. The great initiative in this war is ours. The initiative to stop it must be ours." - Dr. Martin Luther King Jr. =============================================================    (012) _________________________________________________________________ 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    (013) _________________________________________________________________ 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    (014) ```
 Current Thread Re: [ontolog-forum] N-ary relationships and hypergraphs, (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, Ali SH Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart Applications, doug foxvog Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart Applications, Christopher Menzel 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