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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "AzamatAbdoullaev" <abdoul@xxxxxxxxxxxxxx>
Date: Mon, 7 Nov 2011 19:04:38 +0200
Message-id: <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" <dprice@xxxxxxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
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"<david@xxxxxxxxxx>
>> To: "glenn mcdonald"<glenn@xxxxxxxxx>
>> Cc: "AzamatAbdoullaev"<abdoul@xxxxxxxxxxxxxx>;<semantic-web@xxxxxx>;
>> "Frank Manola"<fmanola@xxxxxxx>; "Sampo Syreeni"<decoy@xxxxxx>;
>> <alexandre.riazanov@xxxxxxxxx>
>> 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<abdoul@xxxxxxxxxxxxxx>
>>>> 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<fmanola@xxxxxxx>
>>>> 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.
>>>
>>>
>>
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