Leo,
Re: Yes, very often relations on relations are really rules,
Rules sometimes, yes. But also often "effectivity", authority or provenance. (01)
Note that Conceptual graphs and some other logics have all the capacity needed
to represent N-Relations that can also be the subject of other relations as
John Sowa shows here: http://www.jfsowa.com/cg/cgexampw.htm and here
http://www.jfsowa.com/pubs/laws.htm. This is also a capacity of the IDEAS
framework, SBVR, UML (Association classes) and others. (02)
So this is nothing new, just not a capacity of RDF without reifying everything,
nested graphs models is an approach that doesn't require reifying everything.
Once we can do this (n-relations that can be the subject of other relations)
the "time relation" or other "facets" can then be independent facts operating
on other relations (or situations) such as marriage. The distinction of
"Marriage" as a "situation" or "relation" also seems to go away as relations
can be primitive situations. At some point we have atomic "facts" I would be
interested to know what people think that atomic unit is. (03)
Is there a "fundamental" structure that is always binary? Is it always a
directed binary (e.g. a triple)? I'm not sure. The binary case is certainly
prevalent but only having the binary primitive seems to force unnatural choices
of when to "reify". Federation means never having to say I'm sorry, I didn't
reify it or I didn't add the inverse predicate. (04)
Whatever this fundamental structure is it cannot and does not need to be
complex as it is prevalent and common in communication, language and
information repositories. It seems like we make it complex by optimizing for
either efficient storage or ease of inference. The other choice is to optimize
for expressing information. (05)
By the way, there is a discussion of the "Marriage" use case here:
http://www.omgwiki.org/architecture-ecosystem/doku.php?id=composite_concepts (06)
I will probably add the nice FOL expression provided by doug foxvog. (07)
-Cory (08)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Obrst, Leo J.
Sent: Monday, November 07, 2011 5:23 PM
To: doug@xxxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and
Smart Applications (09)
Yes, very often relations on relations are really rules, as Doug says. (The old
"facet" notion in frame-based ontology languages was the kind of notion Cory
has in mind, I think). In fact one way to think about rules is that they are
relation-generating, through the equivalent of "joins" of predicates. (010)
Of course, what licenses them is the consequence relation at the meta-level.
The transitive pattern P(X, Y), P(Y,Z) |- P(X,Z) , e.g., substitute
'ancestorOf' for P. Or P(X, Y), Q(Y,Z) |- P(X,Z), where 'ancestorOf' is P, and
'parentOf' is Q, and you've probably already defined Q to be the base case of
the recursive P, i.e., parentOf(X,Y) |- ancestorOf(X,Y). Not every Q will do in
the latter, of course; say where 'hasDog' is Q: ancestorOf(X,Y), hasDog(Y,Z) |-
ancestorOf(X,Z). (011)
Thanks,
Leo (012)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of doug foxvog
Sent: Saturday, November 05, 2011 11:24 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and
Smart Applications (013)
On Fri, November 4, 2011 14:02, Cory Casanave said:
> The other strong use-case for reification, besides n-ary, is to
> support relations as first-class elements that can also be the subject
> of other relations. I have found this essential to represent the
> concepts of a domain accurately - "marriage" is such a relation. (014)
In ontological terms, Marriage is a temporal situation.
"isCurrentlyMarriedTo" is a relation -- in this case a binary relation.
Beginning ontologists often start creating binary and multiple arity relations
to represent sets of columns in a database, not stopping to consider what the
underlying classes of things are and realizing that many more relations could
apply to those classes of things in various circumstances. Events and
situations are common categories of things that are often so modeled. (015)
Conceptually higher-arity relations are relations among multiple things that
are more than the sum of their parts, e.g. (between X Y Z) and (betweenOnPath Y
X Z P1). (016)
> The other use-case for
> relations of relations to add metadata about the assertion, including
> the authority and time for which the relation is valid. (017)
This is a useful case for reifying assertions. (018)
The concept of "relations of relations" covers relations which can be mapped
into rules relating assertions on statements using one relation to assertions
on statements using the other relation. E.g.,
* subRelations
(subRelations parentOf relativeOf)
* transitiveClosure
(transitiveClosure parentOf ancestorOf)
* disjointRelations
(disjointRelations youngerThan ancestorOf) (019)
-- doug foxvog (020)
> The problem with this
> in RDF/OWL properties is that the same concept may need, at times, to
> be a reified relation but in simpler cases a single property will do.
> So a general representation seems to always need to use reification.
> On the down-side reification (in RDF/OWL) makes queries much more
> complex and it removed the relations from any "normal" inference as
> they are not asserted in the same way.
>
> For these reasons I have concluded that the simpler approach is for
> all relations to be "first class" so that these artificial differences
> don't exist. Once that simplification is made the logic &
> infrastructure can support all relations consistently and efficiently.
>
> -Cory
>
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed
> Barkmeyer
> Sent: Friday, November 04, 2011 12:32 PM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic
> Web and Smart Applications
>
> The practice of reifying relations in binary models goes back at least
> to Peter Chen and the original Entity-Relationship models.
>
> That is, you make the relation itself a 'class'/'entity', and then it
> has binary relationships to each of its arguments. Each of those
> binary relationships is a term for the 'role' -- the 'argument name'
> if you will, or in the least informative of cases, just the position number.
>
> This is precisely the recommended best practice for representing n-ary
> relationships in OWL: the relation becomes a 'class', and each of the
> argument slots becomes an objectProperty (or datatypeProperty) named
> for the role. The domain of the argument property is the relation
> class and the range of the argument property is the range of the
> argument. One can create the inverse of the role property where it is
> useful, i.e., where one needs to navigate the model from one argument
> of the relation to another.
>
>
> The problem the RDF folk and the OWL folk have is the absence of a way
> to declare that the 'class' term represents an n-ary relation. That
> is the one semantic addition that is created by the UML AssociationClass.
>
> Unfortunately, the other rules for handling association classes in UML
> v1 made the structure hard to use, and many UML best practice
> documents forbid its use. The problem for slavishly object-oriented
> models is whether there is a difference between the role links and the
> attributes of the would-be class, and whether a class whose instances
> play one of the roles has an attribute that refers directly to another
> role player, and of course, what the resulting C++, C# and Java
> implementations will look like. An alternative used by database
> modelers in UML v2 is to create a <n-ary relation> stereotype for
> classes representing reified relations and a <role> stereotype for the
> arguments. The advantage of this approach is that it allows the
> modeler to mark up the model to characterize participation multiplicities
>correctly, and to create the useful inverses.
> And for database models, it distinguishes the functional arguments
> (the role players and their keys) from the dependent variables (the
> other attributes and associations) in the 3rd normal form re lation.
>
> All of this only says that the practice of reification of relations is
> common, but has evolved differently for different implementation
> mechanisms and for different semantic concerns. And make no mistake:
> Tableaux reasoning is an implementation mechanism, and more than half
> of the RDF folk are more worried about managing triple stores than
> manipulating their semantics.
>
> -Ed
>
> P.S. I now await John Sowa's further elaboration/correction on the
> history of reification. :-)
>
> --
> Edward J. Barkmeyer Email: edbark@xxxxxxxx
> National Institute of Standards & Technology Manufacturing Systems
> Integration Division
> 100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
> Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800
>
> "The opinions expressed above do not reflect consensus of NIST, and
> have not been reviewed by any Government authority."
>
>
> 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.
>>
>> 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-knowl
>>>>> edge-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&r
>>>>> ep=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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>>
>> --
>> Managing Director and Consultant
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doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (022)
"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.
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