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

To: <doug@xxxxxxxxxx>, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "AzamatAbdoullaev" <abdoul@xxxxxxxxxxxxxx>
Date: Mon, 7 Nov 2011 23:54:00 +0200
Message-id: <54E914AD589C47CCB7D313B368CE6DDD@personalpc>

----- Original Message ----- 
From: "doug foxvog" <doug@xxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
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" <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
>
>
>> 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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>>
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=============================================================
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)


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