Dear Cory, (01)
With respect to your "atomic facts" ("elementary events" in NKRL), and
the way of "binding" them into second order structures representing
complex events/situations, you should have a look at NKRL 'Narrative
Knowledge Representation Language). You can see my 2009 book,
http://www.springer.com/computer/ai/book/978-1-84800-077-3; recent
papers can also be found at
http://www.sciencedirect.com/science/article/pii/S0950705111000761
(Knowledge-Based Systems, KNOSYS) and
http://www.inderscience.com/search/index.php?action=record&rec_id=42487&prevQuery=&ps=10&m=or (02)
(International Journal of Metadata, Semantics and Ontologies, IJMSO).
You will also find there a discussion about the n-ary problem. I can
send you, in case, personal copies of these papers. (03)
Regards, (04)
Gian Piero ZARRI
Univ. Paris-Est/UPEC, LiSSi Lab.
zarri@xxxxxxx, gian-piero.zarri@xxxxxxxx (05)
On 08/11/2011 05:16, Cory Casanave wrote:
> Leo,
> Re: Yes, very often relations on relations are really rules,
> Rules sometimes, yes. But also often "effectivity", authority or provenance.
>
> 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.
>
>
> 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.
>
> 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.
>
> 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.
>
> By the way, there is a discussion of the "Marriage" use case here:
> http://www.omgwiki.org/architecture-ecosystem/doku.php?id=composite_concepts
>
> I will probably add the nice FOL expression provided by doug foxvog.
>
> -Cory
>
> -----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
>
> 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.
>
> 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).
>
> Thanks,
> Leo
>
> -----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
>
> 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.
> 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.
>
> 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).
>
>> 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.
> This is a useful case for reifying assertions.
>
> 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)
>
> -- doug foxvog
>
>> 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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>>>
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>>> Managing Director and Consultant
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>
> =============================================================
> doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org
>
> "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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