Views on when to use n-ary relations greater than binary - knowledge representation

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Robert Rovetto

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Sep 10, 2021, 2:28:50 AM (11 days ago) Sep 10
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All,

(without being restricted to any particular knowledge representation and reasoning language, because some are restricted only to binary, and some have design patters under that circumstance)

What's your view on:
- when to create a greater-than-binary relation rather than a binary relation?

Consider: you want to represent some information, statement, or knowledge, without necessarily being forced to limit to binary relations. A common example is when wanting to reference time. And 'between' is greater than binary.
What are other pieces of knowledge that you'd want assert a ternary, or greater than binary relation to capture it accurately?

Do you have any rules of thumb for knowing when to assert n-ary relations greater than binary?

Robert
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Azamat Abdoullaev

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Sep 10, 2021, 5:43:21 AM (11 days ago) Sep 10
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Whenever you go for reality and nonlinearity, you need n-relations, as a POSET, chains, tree-like ordering, cycles and networks. A binary relation is just a poor approximation. It was discussed a decade ago. http://ontolog.cim3.net/forum/ontolog-forum/2011-11/msg00085.html

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Igor Toujilov

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Sep 10, 2021, 12:38:36 PM (10 days ago) Sep 10
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Hi Robert,

Depending on practical use cases people use binary or n-ary relations. They even use unary relations almost in all cases. Some people do not realise they use unary relations: for example, asserting an instance of a class.

The rule of thumb for using n-ary relations where n>2 is pretty trivial: use it if you cannot use just unary and/or binary ones. However, I think you know that any n-ary relation where n>2 can be represented as a combination of unary and/or binary relations.


Cheers,

Igor



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Michael DeBellis

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Sep 10, 2021, 2:48:01 PM (10 days ago) Sep 10
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I agree with Igor. I use n-ary relations all the time just modeled as binary relations with additional classes.  One thing I don't understand from some of the arguments for things like RDF* is the idea that n-ary relations are a deficiency in standard RDF and OWL when the semantics are the same whether you implement them as n-ary properties or binary properties with additional classes. This isn't new with OWL either, it is one of the fundamental patterns of  OOP. 

Michael

Michael DeBellis

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Sep 10, 2021, 4:42:38 PM (10 days ago) Sep 10
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There is a good recent overview paper on Knowledge Graphs: https://arxiv.org/pdf/2003.02320.pdf  This has a good discussion of property graphs (direct implementation of n-ary relations) and RDF/OWL (implementing n-ary relations as binary) in section 2.1

Alex Shkotin

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Sep 11, 2021, 3:59:42 AM (10 days ago) Sep 11
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Robert,

One way to get a lot of n-ary relations is to look at any relational DB - there is a lot there - any table is an n-ary relation. If we map a row to a sentence we get a proposition. And visa versa any propositional sentence gives n-ary relation as in Executable English, as far as I remember:-)

Alex

пт, 10 сент. 2021 г. в 09:28, 'Robert Rovetto' via ontolog-forum <ontolo...@googlegroups.com>:
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sowa @bestweb.net

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Sep 11, 2021, 4:37:36 PM (9 days ago) Sep 11
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Michael,
 
That 136-page article can be boiled down to one sentence of useful information:
 
"If you map your pet notation to and from Common Logic, the tools for the DOL standard will map it to any other format you might need."
 
See the following slides:  http://jfsowa.com/talks/eswc.pdf
 
These slides are an extended version of the slides that got the Best Presentation award at the 2020 KGC (Knowledge Graph Conference hosted by Columbia U.).  That was in March 2020.  In June 2020, I presented an extended version in a keynote talk at the European Semantic Web Conference.  In August 2021, I included a subset of them in my Ontolog Forum talk on Universal Query Language.  Since then, I added a new Section 6:  http://jfsowa.com/talks/uql.pdf
 
With the DOL standard, each group that has any special notation just provides a mapping to and from a subset of Common Logic.  Then anybody who prefers any other notation just uses the DOL tools to share data with you.
 
You can recycle those 136 useless pages.
 
John
 
 
 

From: "Michael DeBellis" <mdebe...@gmail.com>
Sent: Friday, September 10, 2021 4:43 PM

Sheth, Amit

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Sep 11, 2021, 7:08:24 PM (9 days ago) Sep 11
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I thought I would share the state of the Semantic Web tech exactly 20 years ago. On 09/11/2001 I gave this keynote in Erfurt, Germany
https://lnkd.in/dNzkTY35 (I was running Taalee/Voquette/Semagix founded in 1999 then).
Starting slide 35, I described our commercial #semanticsearch engine that used a large, 25 domain #knowledgegraph (slides 22, 53; also called WorldModel/ontology in the patent) which also supported the concept of KG enhanced Semantic Enrichment we called Rich Media Object (slides 46-49) - the concept was seen again in 2013 as Infobox in Google Semantic Search. Details at: https://lnkd.in/eKX2maV

ps: The rest of the day was unexpectedly eventful. I decided to leave early instead of staying for the conference, took the fast train to reach Frankfurt airport arriving 15-20 minutes before the departure of my flight, bypassed the counter - because I was a platinum premier, they opened the door that had just been closed. Wish I had missed the flight. Just west of Ireland's west coast over the Atlantic, the plane dumped fuel and landed at Dublin along with many other flights. You can image the rest.

doug foxvog

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Sep 13, 2021, 1:59:08 AM (8 days ago) Sep 13
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Sure, one can always make an n-ary relation more complex by reifying the
situation of the n-ary relation being true as an object and then relating
each argument place to that object with a specific binary relation. This
can be valuable if one wants to provide more information about that
situation -- which would be otherwise considered meta-data about the n-ary
relation assertion.

Needless to say, adding this complexity takes more memory and more
processing time.

Of course, one could do the same with existing binary relations -- reify
an assertion using them as an object and using 2 different binary
relations to relate the first and second argument to the reified object.
The utility of both seem the same to me.

E.g., (motherOf Juan Maria) => Exists (X; (AND (motherhoodSituation X)
(motherInSituation X Maria) (childInSituation X Juan)). If X is reified,
then additional information such as starting time, who knows X, who
reported X, the record # for X in a database Y, etc.

Yes, the above complicates expressing (motherOf Juan Maria), just as
breaking an n-ary (n > 2) relation into binary relations does.

I note that most databases use more than two columns. and that the
multiple columns often do not express binary relations. A shopping
database might have columns for store, date, product type, number of items
of type sold at full price, number of items of type sold at discount,
discount percentage, number of items returned, department of store, and
other columns. It is easy to express this as multiple n-ary relations
which a computer program can process to generate statistics and make
logistical decisions over hundreds of thousands of lines in the DB.
Reifying multiple objects for each line (millions total) to do the
processing would be an added complexity. -- especially since such objects
would have no utility after the desired calculations are made.

The only advantage in expressing n-ary relation as a set of binary
relations seems to me that it allows one to use a deficient language to
express them. I try to avoid such for the same reasons that i do not code
using actual Turing Machines. They are the wrong tool for the job, and as
such take more complexity and memory than using a tool that better fits
the problem.

-- doug foxvog

> On Friday, September 10, 2021 at 11:48:01 AM UTC-7 Michael DeBellis
> wrote:
> I agree with Igor. I use n-ary relations all the time just modeled as
> binary relations with additional classes. One thing I don't understand
> from some of the arguments for things like RDF* is the idea that n-ary
> relations are a deficiency in standard RDF and OWL when the semantics are
> the same whether you implement them as n-ary properties or binary
> properties with additional classes. This isn't new with OWL either, it is
> one of the fundamental patterns of OOP.
> Michael
>
> On Friday, September 10, 2021 at 9:38:36 AM UTC-7 Igor Toujilov wrote:
>
> Hi Robert,
>
> Depending on practical use cases people use binary or n-ary relations.
> They even use unary relations almost in all cases. Some people do not
> realise they use unary relations: for example, asserting an instance of a
> class.
>
> The rule of thumb for using n-ary relations where n>2 is pretty
> trivial: use it if you cannot use just unary and/or binary ones.
> However, I think you know that any n-ary relation where n>2 can
> be
> represented as a combination of unary and/or binary relations.
>
>
>
> Cheers,
>
> Igor
>
>
>
> --
> All contributions to this forum are covered by an open-source license.
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> https://groups.google.com/d/msgid/ontolog-forum/88b90be93cf0438688106de6923aacfe%40bestweb.net.
>


Alex Shkotin

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Sep 13, 2021, 5:06:06 AM (8 days ago) Sep 13
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Robert,

Let me underline an important point: first of all, we have found in nature and society one or another relation and ask how many members each example of this relation can have? i.e. arity is a feature of relation itself. 
so,
"when to create a greater-than-binary relation rather than a binary relation?" - when relation itself is n-ary.
"Do you have any rules of thumb for knowing when to assert n-ary relations greater than binary?" - we come here to the logic of relations and its discovery. For me, examples of relations of different arity from one or another domain would be great.

What about [1]?

Alex



пт, 10 сент. 2021 г. в 09:28, 'Robert Rovetto' via ontolog-forum <ontolo...@googlegroups.com>:
All,
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Jon Awbrey

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Sep 13, 2021, 5:24:25 AM (8 days ago) Sep 13
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Well, at least now I know why the Web is making people stupider day by day …

Regards,

Alex Shkotin

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Sep 13, 2021, 7:25:38 AM (8 days ago) Sep 13
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:-)

пн, 13 сент. 2021 г. в 12:24, Jon Awbrey <jaw...@att.net>:

Jon Awbrey

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Sep 13, 2021, 8:48:46 AM (8 days ago) Sep 13
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Re: https://www.w3.org/TR/swbp-n-aryRelations/

I know, I tell myself, calm down, Jon, it's just a tutorial doc from 15 years ago ...
but every time I see someone using “reification” that way it just makes we want to
go back on Facebook and argue with Trumplodytes or anything else less dispiriting ...

At any rate, for what it's worth, as we used to say ...

Here's a first introduction to k-adic or k-ary relations from a mathematical perspective.

Relation Theory
https://oeis.org/wiki/Relation_theory

Here's a few additional resources and assorted discussions with folks around the web.

Survey of Relation Theory
https://inquiryintoinquiry.com/2020/05/15/survey-of-relation-theory-4/

More than anything else it's critical to understand the differences among:

1. The relation itself, which is a mathematical object,
a subset embedded in a cartesian product of several
sets called the “domains” of the relation.

2. The individual k-tuple, sometimes called an elementary relation,
a single element of the relation and hence the cartesian product.

3. The syntactic forms, lexical or graphical or whatever,
used to describe elements and subsets of the relation.

4. The real phenomena and real situations, empirical or hypothetical,
we use mathematical objects such as numbers, sets, functions, groups,
algebras, manifolds, relations, etc. to model, at least approximately
and well enough to cope with their realities in practice.

Regards,

Jon
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William Frank

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Sep 13, 2021, 10:24:43 AM (8 days ago) Sep 13
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Alex,

Well said!  

I was going to reply to the question and some of the answers with my semi-yearly rant about the reductionist unexamined belief that if something *can* be expressed using a smaller syntax, then it *really* is the translated expression, rather than what was said.   In my case, all the logic students who seem to have "learned" that there 'really is' only one truth functional connector: 'nor', when we find almost a dozen in human reasoning, and when there is no given reason to prefer one minimal set of these rather than another as more fundamental than any other.    

I might add to your advice:  'if you have n-ary relations in your language, use them for n-ary relations in the langauge your are modelling!   If not, then translate them if you can to what you *do* have in some standard way. 

Wm   

sowa @bestweb.net

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Sep 14, 2021, 12:01:28 AM (7 days ago) Sep 14
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Doug,
 
I agree with that point:
 
 
DF:  Sure, one can always make an n-ary relation more complex by reifying the
situation of the n-ary relation being true as an object and then relating
each argument place to that object with a specific binary relation. This
can be valuable if one wants to provide more information about that
situation -- which would be otherwise considered meta-data about the n-ary
relation assertion.
 
For example, the verb 'give' has three obligatory arguments:  Agent, Theme, and Recipient.  In linguistics, the links to those arguments may be represented by binary "case relations" or "thematic roles".  Then the syntax for any natural language can be related to those relations.
 
But this is a principled reason for introducing those relations.  In general, people should study the subject matter to determine when, whether, why, and how to add such features.
 
John

Alex Shkotin

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Sep 14, 2021, 6:02:39 AM (7 days ago) Sep 14
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William,

Math is a world of metamorphosis, polymorphisms, and so on. Just amazing :-)

Alex

пн, 13 сент. 2021 г. в 17:24, William Frank <william...@gmail.com>:

Alex Shkotin

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Sep 14, 2021, 6:30:47 AM (7 days ago) Sep 14
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Jon,

IMHO we should begin from your p.4 calling the math we need. So let's take case 3 from the tutorial you refer to:"
  1. John buys a "Lenny the Lion" book from books.example.com for $15 as a birthday gift. There is a relation, in which individual John, entity books.example.com and the book Lenny_the_Lion participate. This relation has other components as well such as the purpose (birthday_gift) and the amount ($15).
"
We have here the action done by John with the purpose of action in the future - as a birthday gift. As they pointed out we have individual, entity, book, $15, and birthday in the future. Are they related? Yes! How? Well, goto 1. But there is no relation they mentioned here at all unless they invent it consciously. This is from the RDB paradigm I think:-)

Alex

пн, 13 сент. 2021 г. в 15:48, Jon Awbrey <jaw...@att.net>:
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Giancarlo Guizzardi

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Sep 14, 2021, 7:13:03 AM (7 days ago) Sep 14
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Dear colleagues,

It has been hard to keep track of all details of the discussions.
In any case, perhaps the following papers can be of use somehow to a discussion about ontological aspects of relations:


The point here is not about arity, but differentiating categories of relations based
on the nature of their truthmakers.

best regards,
Giancarlo Guizzardi



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Aldo Gangemi

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Sep 14, 2021, 7:35:41 AM (7 days ago) Sep 14
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… and that’s a chapter from the "Ontology Engineering with Ontology Design Patterns” book, about alternative representations of multi-varied predicates (n-ary relations), with pros and cons. The chapter addresses both extensional and intensional relations:


Best
Aldo




________________________________

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University of Bologna

Director
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National Research Council (ISTC-CNR)




dr.matt...@gmail.com

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Sep 14, 2021, 8:45:45 AM (7 days ago) Sep 14
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OK. I can’t resist any more. Lots of interesting stuff here, but the basic problem is that most of it conflates relationships/situations/activities with relations. They are not the same thing. Relationships (for example) are what one thing has to do with another (or itself) and the other is a mathematical structure that is often found useful in representing the first (and there are choices about how to do that).

Regards

Matthew West

Giancarlo Guizzardi

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Sep 14, 2021, 9:31:41 AM (7 days ago) Sep 14
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Matthew,

I agree that relationship is "what one thing has to do with another" but we deny that this thing is (necessarily) a mathematical tuple.
In fact, for the most interesting material relationships, these "things" are concrete full-fledged endurants (e.g., marriages, enrollments, employments, presidential mandates).
The key to the analysis is understanding the nature of this mediating "thing" as the grounding of relations (relations hold, relationships exist)
and truthmakers of relational propositions.

Two other papers that might be useful in that respect are:

In the background of all this, and with a more philosophical guise
is our theory of "weak truthmaking": http://www.inf.ufes.br/~gguizzardi/truthmaking2019.pdf

best,
Giancarlo

PS: Thanks for the very nice talk at OntoCom yesterday

Chris Partridge

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Sep 14, 2021, 1:02:33 PM (6 days ago) Sep 14
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Hi Giancarlo,

The interesting question is whether these things "(e.g., marriages, enrollments, employments, presidential mandates)" are event objects in their own right - or somehow dependent relations.
Aldo's paper makes the point - noting of course, Davidson (D. Davidson. The Logical Form of Action Sentences. In The Logic of Decision and Action. University of Pittsburgh Press, Pittsburgh, 2nd edition, 1967.)
And also, the issues of multigradeness if treating them as relations - A. Oliver and T. Smiley Multigrade Predicates Mind, 113, 2004.

Chris

Giancarlo Guizzardi

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Sep 14, 2021, 1:23:28 PM (6 days ago) Sep 14
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Hi Cris,

That is an interesting question but not the only one. As you will see in the paper, our view is that they are not events (we actually explicitly reject) that. As you know, we tridimensionalists and we believe these things can genuinely chance “as a whole” like any other endurant.

Best,
G

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William Frank

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Sep 14, 2021, 2:54:36 PM (6 days ago) Sep 14
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My views about this may be naive, perhaps because of my predilection to consider thought as expressed in natural languages to be the subject under study, while relations, endurants, occurents, are models of the various ways people have and can experience and think about the same things (in themselves) as phenomena, depending on the semantic conventions in their languages. 

It seems to me this debate is mostly a matter of ways of thinking about things in a given language, rather than what they really are.  For instance, some languages separate masses of a substance, (gold, rice, hair in English) from individuals (beans, grains of rice, hair in French and German).   Hard for me to find cases where something can't be cast as being in one such category or another.  

Aren't there actually two things, governed by laws of duality

Endurants: marriages, enrollments, presidential proclamations, chickens
Occurents: the act of getting married, of enrolling, of proclaiming, the act of hatching, dying, 

So that the marriage endures from the time it occurs to the time of its dissolution, the duality between the two.  Etc. 
And of course since every event takes a length of time, and is not atomic except relative to a given viewpoint, and because some things one might think of most simply as events are treated as endurants - e.g., hurricanes, (after all, we give them names).

Though there are multiple roles in endurants and occurrents, does not prove they are 'really' relations.  It just shows they can be (perhaps only partially) modelled as relations.   What is missing, to me, about the model of an event or an enduant as a relation are the roles of the other things in the conceptual structure.  

 


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Giancarlo Guizzardi

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Sep 14, 2021, 3:06:13 PM (6 days ago) Sep 14
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William,

My position (and I sure Chris would agree) is that these are ontological distinctions.

Language is polysemic and often polysemic in a systematic way. So, the term
Marriage can refer both to an endurant and an event, and these two referents would
bear some systematic relation between them.

What makes a marriage (qua-endurant) relational is the fact that it is
existentially dependent on a multitude of individuals. For example, the specific marriage
of John and Mary is existentially dependent on John and Mary, thus, binding them.
That is why it can be the truthmaker of the relational proposition "John and Mary are married".
If we look inside such an entity, this Marriage (again, qua-endurant) is a bundle of relational
qualities (tropes, modes) that are relational in nature (e.g., John's commitments and claims towards Mary,
and Mary's commitments and claims towards John, etc).

Now, what makes something like a marriage a true endurant is that it has essence and accidents
(like any other endurant). John&Mary's marriage is essentially a marriage but only contingently
a happily marriage, a marriage with full separation of assets, etc.

This is the gist of the idea

best,
Giancarlo


William Frank

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Sep 14, 2021, 4:39:38 PM (6 days ago) Sep 14
to ontolog-forum
Thanks, Giancarlo 

Your simple responses let me understand and see the wisdom of what you guys are saying.

I found this very helpful: 

Now, what makes something like a marriage a true endurant is that it has essence and accidents
(like any other endurant). John&Mary's marriage is essentially a marriage but only contingently
a happily marriage, a marriage with full separation of assets, etc.Thanks, Giancarlo

And this is part of what I was trying to say: 

Language is polysemic and often polysemic in a systematic way. So, the term
Marriage can refer both to an endurant and an event, and these two referents would
bear some systematic relation between them.

And this seems to me to reconcile and clarify what I was claiming about roles being more that 'just' what shows up in an n-tuple.

If we look inside such an entity, this Marriage (again, qua-endurant) is a bundle of relational
qualities (tropes, modes) that are relational in nature (e.g., John's commitments and claims towards Mary,
and Mary's commitments and claims towards John, etc).

I am still at a loss to know what this means: 

My position (and I sure Chris would agree) is that these are ontological distinctions.
Unless an ontological distinction is between different ways that people can see the same experience (for example, as a substance (rice and English hair) or as an individual (a bean, or French hairs). 

I would not be surprised, I must say, if you clarified this, too. 


On Tue, Sep 14, 2021 at 3:06 PM Giancarlo Guizzardi <gguiz...@gmail.com> wrote:
William,

My position (and I sure Chris would agree) is that these are ontological distinctions.

Language is polysemic and often polysemic in a systematic way. So, the term
Marriage can refer both to an endurant and an event, and these two referents would
bear some systematic relation between them.

What makes a marriage (qua-endurant) relational is the fact that it is
existentially dependent on a multitude of individuals. For example, the specific marriage
of John and Mary is existentially dependent on John and Mary, thus, binding them.
That is why it can be the truthmaker of the relational proposition "John and Mary are married".
If we look inside such an entity, this Marriage (again, qua-endurant) is a bundle of relational
qualities (tropes, modes) that are relational in nature (e.g., John's commitments and claims towards Mary,
and Mary's commitments and claims towards John, etc).


Roberto Rovetto

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Sep 14, 2021, 6:02:16 PM (6 days ago) Sep 14
to ontolog-forum
Returning to my original post/questions, please see that (there seem to have been tangents). To supplement and perhaps refocus:

Sometimes rich or complex expressions, sentences, beliefs or pieces of knowledge seem to express what in KRR and associated formal and computational activities would formalize in a greater-than-binary n-ary relation. However, in computational ontology some would model them--as others have already pointed out--using binary relations or patterns. Sometimes this decision is unfortunately forced upon them because of the expressive limitations of the KRR language or formalism (e.g., in OWL).

So I asked what are views when faced with expressions, sentences et al, that seem to express or need creating n-ary relations?
When would you create a greater-than-binary n-ary relation in a computational ontology rather than binary?

In other words...

  • Think of some greater-than-binary relationships. When would you formalize them--create logical or computable relations--as such rather than some other approach (binary or otherwise)? And why?

  • Think of a statement, fact, situation or piece of knowledge that you want to model or represent either in a KRR/ontological manner (i.e. computational focus) OR more abstractly in a purely symbolic logic.
    How would you, personally, determine whether n-ary is needed?
    (An obvious answer, already provided by others, is if there are more than 2 individuals or argument involved. Perhaps it's as simple as that, but i'd like to hear if there is a variety of views and approaches)

  • How would you, personally, decide if to assert binary or greater relations?
    Would it be based on convenience? Or trying to match as accurately or truthfully as possible what is expressed in the sentence or piece of knowledge? etc...?
  • If what you're trying to model seems to involve need of asserting an n-ary relation, or if it explicitly involves phrases that call for the assertion of an n-ary relation, what conditions would incline you to formalize them as such rather than another way?

Robert

P.S. William, this is obviously not the intended topic of my post, but I'll address some of what you asked and said. You are correct in various ways so do not be quick to discount or change your views. For example you wrote: "It seems to me this debate is mostly a matter of ways of thinking about things in a given language, rather than what they really are". Yes--there is much of that. The interplay between our ideas, thoughts, language, and inquiry to understand the world, etc. is complex with many unanswered questions and the literature from philosophy (ancient to contemporary), linguistics, KRR and AI (including ontology engineering), social sciences, etc. shows that. As others on the forum have expressed in one way or another over the years.

The topic and questions associated with endurants/perdurants (and the like) are highly abstract metaphysical/philosophical-ontology concepts and accounts of some phenomena (whether mind-dependent or otherwise)...certainly that is the historical sense that continues in the philosophical discipline to date. That very high abstractness--just like in natural langauge with generic words--means they are often open to interpretation, and certainly have a plethora of metaphysical accounts, and they reflect unanswered (perhaps unanswerable) philosophical question (e.g., for endurants/perdurants it is about time and persistence). Indeed, there are no answers (at least not universally accepted) to the associated questions from which these concepts and accounts are spawned. Some, assume a threedimensional account, others fourdimensional, and others make no explcit assumptions, or different ones. Likewise in this community of a computational focus, some (but certainly not all) ontologies or their developers assume things or make variations.

When these metaphysical concepts are injected--in some form--in this community of a computational focus, there does not need to be (nor should there be as it often muddies things) any metaphysical claims about the world or whatever target subjects being modeled, but rather the focus on computational goals, and things like internal consistency, etc. But moreover, they need not be injected/used in contemporary ontology engineering in any case. And, also given the great generality, new and hybrid concepts and accounts can be made.

Again, there's many such metaphysical accounts, and some computational ontologies (sometimes the most generic ones), as Giancarlo pointed out, use some concepts from these accounts or modify them or assert new concepts for their ontologies. But in the present context (e.g., this forum), putting forth metaphysical accounts is not the goal; metaphysicians and philosophical ontologists do that full-time as it were (and therefore with much greater thoroughness without the expressive limitations of computational formalisms, requirements, etc.). There is a computational focus, so internal consistency, rather than metaphysical claims is primary.

E.g., A marriage, and other things, can be modeled in different ways, and different metaphysical accounts will do so. Likewise, distinct computational ontologies will model them differently. And more generally, distinct persons or groups can model it uniquely.

On Friday, September 10, 2021 at 2:28:50 AM UTC-4 Roberto Rovetto wrote:
All,

(without being restricted to any particular knowledge representation and reasoning language, because some are restricted only to binary, and some have design patters under that circumstance)

What's your view on:
- when to create a greater-than-binary relation rather than a binary relation?

Consider: you want to represent some information, statement, or knowledge, without necessarily being forced to limit to binary relations. A common example is when wanting to reference time. And 'between' is greater than binary.
What are other pieces of knowledge that you'd want assert a ternary, or greater than binary relation to capture it accurately?

Do you have any rules of thumb for knowing when to assert n-ary relations greater than binary?

Robert
--

dr.matt...@gmail.com

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Sep 15, 2021, 2:47:01 AM (6 days ago) Sep 15
to ontolo...@googlegroups.com

Dear Giancarlo,

Yes, I also looked at this some time ago:

West, Matthew Information Modelling: An analysis of the uses and meanings of associations PDT Europe 2002, PDF

And in my book

West, Matthew Developing High Quality Data Models Morgan Kaufmann 2011

Where Chapter 11 has a section on associations (aka situations).

Regards

Matthew West

Giancarlo Guizzardi

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Sep 15, 2021, 4:18:10 AM (6 days ago) Sep 15
to ontolo...@googlegroups.com
Hi William,

What I meant to say with that passage is the following.

1) yes, there are multiple ontological cuts that can be made to reality. For example, a fourdimensionalist such as Chris would
believe that not only John&Mary's marriage but also John and Mary are events. Someone holding my views, in contrast, will
see John, Mary, and John&Mary's Marriage as endurants to which there are events associated that will constitute John's Life, Mary's Life,
John&Mary's Marriage's Life (actually, to each of these endurants, there are associated multiple possible lives but that is a different story -
see ).

2) What I mentioned that both Chris and I would hold is the view that things like John, Mary and John&Mary's Marriage are things
that really exist in the world. So, the piece of language "John&Mary's Marriage" picks up something really out there. Again, for Chris,
this would be an event; for me, this can polysemically refer to both the endurant binding them and one of its possible lives (an event).

3) Here is what I think you mean: we can have different conceptualizations
to the same portion of reality. These conceptualizations would influence perspective, granularity, etc. Given this, we can see a phenomenon
as a portion of blood (an amount of matter) or a collective of individual blood cells. To that I would agree.

Hope I managed to clarify my point

best,
Giancarlo


Giancarlo Guizzardi

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Sep 15, 2021, 4:19:01 AM (6 days ago) Sep 15
to ontolo...@googlegroups.com
Thanks for the pointers, Matthew.
I will definitely look into them

best,
Giancarlo

Giancarlo Guizzardi

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Sep 15, 2021, 4:21:44 AM (6 days ago) Sep 15
to ontolo...@googlegroups.com
Sorry, forgot to past a link in this passage:



On Wed, Sep 15, 2021 at 10:17 AM Giancarlo Guizzardi <gguiz...@gmail.com> wrote:

1) yes, there are multiple ontological cuts that can be made to reality. For example, a fourdimensionalist such as Chris would
believe that not only John&Mary's marriage but also John and Mary are events. Someone holding my views, in contrast, will
see John, Mary, and John&Mary's Marriage as endurants to which there are events associated that will constitute John's Life, Mary's Life,
John&Mary's Marriage's Life (actually, to each of these endurants, there are associated multiple possible lives but that is a different story -
see ).


I mean that the interested reader in what I meant by an "endurant being associated with multiple possible lives"
could find useful to take a look at http://www.inf.ufes.br/~gguizzardi/BPM2016.pdf

best,
G

William Frank

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Sep 15, 2021, 9:42:25 AM (6 days ago) Sep 15
to ontolog-forum

Jon Awbrey

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Sep 16, 2021, 11:00:28 AM (5 days ago) Sep 16
to Ontolog Forum
Cf: Relations & Their Relatives • Discussion 22
https://inquiryintoinquiry.com/2021/09/16/relations-their-relatives-discussion-22/

Re: Ontolog Forum
https://groups.google.com/g/ontolog-forum/c/0pDK8IJiFDc
::: Roberto Rovetto
https://groups.google.com/g/ontolog-forum/c/0pDK8IJiFDc/m/jwg3FbzfBgAJ
https://groups.google.com/g/ontolog-forum/c/0pDK8IJiFDc/m/HrdY9T1QAAAJ

<QUOTE RR:>
What's your view on:

When to create a greater-than-binary relation rather than a binary relation?

Consider: You want to represent some information, statement, or knowledge,
without necessarily being forced to limit to binary relations. A common
example is when wanting to reference time. And “between” is greater than
binary. What are other pieces of knowledge that you'd want assert a ternary,
or greater than binary relation to capture it accurately?

Do you have any rules of thumb for knowing when
to assert n-ary relations greater than binary?
</QUOTE>

Dear Roberto,

Let me return to your original question and give it better attention.

You have probably noticed you got a wide variety of answers coming from
a diversity of conceptual frameworks and philosophical paradigms. It
gradually dawned on me some years ago these differences are most likely
matters of taste about which all dispute is futile, however much we go
ahead and do it anyway. So I'll just say what I've found works best in
my particular applications of interest, namely, applying relational logic
to mathematics and research sciences.

To avoid the kinds of culture clashes I remember from the
Standard Upper Ontology Lists and other ancestors of this
Forum at the turn of the millennium, I'll develop the rest
of this line of inquiry on the Relations & Their Relatives
thread ( https://groups.google.com/g/ontolog-forum/c/cL22KqWr8PI )
and, as I usually do, post better-formatted copy on my blog
( https://inquiryintoinquiry.com/ ).

Regards,

Jon

Michael DeBellis

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Sep 16, 2021, 11:22:00 AM (5 days ago) Sep 16
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You have probably noticed you got a wide variety of answers coming from
a diversity of conceptual frameworks and philosophical paradigms.  It
gradually dawned on me some years ago these differences are most likely
matters of taste about which all dispute is futile, however much we go
ahead and do it anyway. 

Exactly. One thing I learned the hard way is that there is no perfect model,  you can always model a domain in multiple ways and thrashing around looking for the model that is the "real" model leads to analysis paralysis.  Every methodology that is any good always emphasizes this. Also, I think most of these discussions are pointless in another more important way: when you do actual software development they almost never come up and if they do a good team leader shuts them down really quickly.  You will be constrained on any real project to use some sort of modeling paradigm: UML, OWL, etc. That paradigm (and methodologies associated with it) will typically define what kind of formalisms you have to work with and when to use what.  

Michael

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doug foxvog

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Sep 16, 2021, 11:00:09 PM (4 days ago) Sep 16
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On Tue, September 14, 2021 18:02, 'Roberto Rovetto' via ontolog-forum wrote:
> Returning to my original post/questions, please see that (there seem to
> have been tangents). To supplement and perhaps refocus:
>
> Sometimes rich or complex expressions, sentences, beliefs or pieces of
> knowledge seem to express what in KRR and associated formal and
> computational activities would formalize in a greater-than-binary n-ary
> relation. However, in computational ontology some would model them--as
> others have already pointed out--using binary relations or patterns.
> Sometimes this decision is unfortunately forced upon them because of the
> expressive limitations of the KRR language or formalism (e.g., in OWL).
>
> So I asked what are views when faced with expressions, sentences et al,
> that seem to express or need creating n-ary relations?
> When would you create a greater-than-binary n-ary relation in a
> computational ontology rather than binary?
>
> In other words...
>
>
> - Think of some greater-than-binary relationships. When would you
> formalize them--create logical or computable relations--as such rather
> than
> some other approach (binary or otherwise)? And why?

I would use an n-ary relation when the knowledge i wish to model has more
than two arguments and there seems no need to reify a permanent object to
model that knowledge. If the binary relations themselves had little
intrinsic meaning i would avoid creating them.

If i had a simple database with columns:
STORE DEPT PROD# AmountSold SalesAmount Week
for all the stores in a chain for all the weeks in a quarter, i would want
relations:
* weeklySalesByProductAndStore (4-ary)
* weeklySalesAmtByProductAndStore (4-ary)
* storeProductDepartment (3-ary)
Using them, i would want to calculate other n-ary relations:
* quarterlySalesByProductAndStore (4-ary)
* quarterlySalesAmtByProductAndStore (4-ary)
* weeklySalesByProduct (3-ary)
* weeklySalesAmtByProduct (3-ary)
* quarterlySalesByProduct (3-ary)
* quarterlySalesAmtByProduct (3-ary)
* averagePriceOfProductAtStoreByDate (4-ary)
I would allow most of these to use more general product type at many
levels. E.g., 6 oz. peach Organiq (tm) yogurt => peach Organiq yogurt, 6
oz. peach yogurt, => flavored Organiq yogurt, 6 oz flavored yogurt, peach
yogurt => Organiq yogurt, 6 oz. yogurt, flavored yogurt => yogurt => dairy
product, etc.

If i did not have n-ary relations, i would have to reify an object for
each of the hundreds of thousands (or millions) of uses of these relations
just to express binary relations about them. And the binary relations by
themselves would have little meaning.

-- doug foxvog

> - Think of a statement, fact, situation or piece of knowledge that you
> want to model or represent either in a KRR/ontological manner (i.e.
> computational focus) OR more abstractly in a purely symbolic logic.
> How would you, personally, determine whether n-ary is needed?
> (An obvious answer, already provided by others, is if there are more
> than 2 individuals or argument involved. Perhaps it's as simple as
> that,
> but i'd like to hear if there is a variety of views and approaches)
>
> - How would you, personally, decide if to assert binary or greater
> relations?
> Would it be based on convenience? Or trying to match as accurately or
> truthfully as possible what is expressed in the sentence or piece of
> knowledge? etc...?
>
>
> - If what you're trying to model seems to involve need of asserting an
>> *Actively open to work and PhD study opportunities, worldwide.*
>>
>> *-*
>> OntologPage <https://ontologforum.org/index.php/RobertRovetto>
>> IAOA Education Committee
>> Contact <https://ontospace.wordpress.com/contact/>
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>
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>


doug foxvog

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Sep 16, 2021, 11:24:08 PM (4 days ago) Sep 16
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On Wed, September 15, 2021 04:17, Giancarlo Guizzardi wrote:
> Hi William,
>
> What I meant to say with that passage is the following.
>
> 1) yes, there are multiple ontological cuts that can be made to reality.
> For example, a four-dimensionalist such as Chris would
> believe that not only John&Mary's marriage but also John and Mary are
> events. Someone holding my views, in contrast, will
> see John, Mary, and John&Mary's Marriage as endurants to which there are
> events associated that will constitute John's Life, Mary's Life,
> John&Mary's Marriage's Life (actually, to each of these endurants, there
> are associated multiple possible lives but that is a different story -
> see ).

Note that if one can reify both events and endurants, then both of you can
reify the same objects: John, Mary, John&Mary'sMarriage, John'sLife,
Mary'sLife, John&Mary'sMarriage'sLife.

One then defines these objects as instances of the same classes: Person,
Marriage, Person'sLife, Marriage'sLife. These can be agreed to be
subclasses of the same superclasses: Animal, Agreement, Animal'sLife,
Agreement'sLife. At some higher level, the ontologies would separate into
whether things are events or endurants (if desired).

> 2) What I mentioned that both Chris and I would hold is the view that
> things like John, Mary and John&Mary's Marriage are things
> that really exist in the world. So, the piece of language "John&Mary's
> Marriage" picks up something really out there. Again, for Chris,
> this would be an event; for me, this can polysemically refer to both the
> endurant binding them and one of its possible lives (an event).

This is no problem. It does not have to force itself at the level of the
individual or the immediate classes that each individual is an instance
of.

> 3) Here is what I think you mean: we can have different conceptualizations
> to the same portion of reality. These conceptualizations would influence
> perspective, granularity, etc. Given this, we can see a phenomenon
> as a portion of blood (an amount of matter) or a collective of individual
> blood cells. To that I would agree.

Agreed.

-- doug foxvog
>>>>>>>> *From:* 'Aldo Gangemi' via ontolog-forum <
>>>>>>>> ontolo...@googlegroups.com>
>>>>>>>> *Sent:* 14 September 2021 12:36
>>>>>>>> *To:* ontolo...@googlegroups.com
>>>>>>>> *Cc:* Aldo Gangemi <gan...@mac.com>
>>>>>>>> *Subject:* Re: [ontolog-forum] Views on when to use n-ary
>>>>>>>> relations
>>>>>>>> greaterthanbinary - knowledge representation
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> … and that’s a chapter from the "Ontology Engineering with
>>>>>>>> Ontology
>>>>>>>> Design Patterns” book, about alternative representations of
>>>>>>>> multi-varied
>>>>>>>> predicates (n-ary relations), with pros and cons. The chapter
>>>>>>>> addresses
>>>>>>>> both extensional and intensional relations:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> https://www.dropbox.com/s/y73e7qk0nja9zxw/multilayered-nary-patterns-odpbook.pdf?dl=0
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Best
>>>>>>>>
>>>>>>>> Aldo
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> ________________________________
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Aldo Gangemi
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Full professor
>>>>>>>> University of Bologna
>>>>>>>>
>>>>>>>> Via Zamboni 32 40126, Bologna, Italy
>>>>>>>> <https://www.google.com/maps/search/Via+Zamboni+32%C2%A040126,+Bologna,+Italy?entry=gmail&source=g>
>>>>>>>> <https://groups.google.com/d/msgid/ontolog-forum/5de3b00f56c941d0b54a46131284977c%40bestweb.net?utm_medium=email&utm_source=footer>
>>>>>>>> .
>>>>>>>>
>>>>>>>>
>>>>>>>>
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>>>>>>>> .
>>>>>>>>
>>>>>>>>
>>>>>>>>
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doug foxvog

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Sep 17, 2021, 12:43:28 AM (4 days ago) Sep 17
to ontolo...@googlegroups.com
On Tue, September 14, 2021 16:38, William Frank wrote:
> Thanks, Giancarlo
>
> I found this very helpful:
>
>> Now, what makes something like a marriage a true endurant is that it has
>> essence and accidents
>> (like any other endurant). John&Mary's marriage is essentially a marriage
>> but only contingently
>> a happily marriage, a marriage with full separation of assets, etc.
>> Thanks, Giancarlo
>
> And this is part of what I was trying to say:
>...
> Marriage can refer both to an endurant and an event, and these two
> referents would bear some systematic relation between them.
> ...

Events are rarely instantaneous. They normally have a starting and ending
time, and thus endure for some period of time.

For me, i normally use the word "situation" for relatively static states
of affairs, and restrict my use of the word "event" to a subclass of
"situation" in which change is important throughout its duration.

But i understand the term "event" is used above for what i would call a
"situation".

A marriage is a situation that is useful to reify, since there is a lot to
say about it. The marriage starts with a subevent called a wedding and
ends with an event such as a death or divorce. Complex rules can be
created dealing with marriages

(implies
(and
(isa ?LAW BigamyLaw)
(isa ?MAR1 Marriage)
(isa ?MAR2 Marriage)
(partyTo ?MAR1 ?PERSON)
(partyTo ?MAR2 ?PERSON)
(partyTo ?MAR1 ?P2)
(partyTo ?MAR2 ?P3)
(different ?PERSON ?P2 ?P3) ; all 3 are different
(temporalExtent ?MAR1 ?PERIOD1)
(temporalExtent ?MAR2 ?PERIOD2)
(temporalExtent ?LAW ?PERIOD3)
(temporalOverlap ?PERIOD1 ?PERIOD2 ?PERIOD3 ?OVERLAP)
; ?OVERLAP is the temporal overlap of the 3 preceding time periods
(jurisdictionRegion ?LAW ?REGION)
(inRegionSometimeDuring ?PERSON ?REGION ?OVERLAP))
(inViolation ?PERSON ?LAW))
This says that a person is in violation of a bigamy law if they are in the
jurisdiction covered by that law at a time the law is in effect and they
are party to two marriages (or a marriage with at least 3 parties).

It would be more complex to write such a rule if marriages were not
reified or if only binary relations could be used.

-- doug f

doug foxvog

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Sep 17, 2021, 12:54:07 AM (4 days ago) Sep 17
to ontolo...@googlegroups.com
On 14 September 2021 14:31, Giancarlo Guizzardi wrote:

> I agree that relationship is "what one thing has to do with another" but
> we deny that this thing is (necessarily) a mathematical tuple.

This is in fact in agreement with Matthew West, who said (below):
>> the basic problem is that most of [referenced discussion] conflates
>> relationships ... with relations. ...
>> [A relationship] is a mathematical structure that is often
>> found useful in representing the [relation]

> In fact, for the most interesting material relationships, these "things"
> are concrete full-fledged endurants (e.g., marriages, enrollments,
> employments, presidential mandates).

It appears the three of us agree.

> The key to the analysis is understanding the nature of this mediating
> "thing" as the grounding of relations (relations hold, relationships
> exist)

> and truthmakers of relational propositions.

-- doug foxvog
> aldo.g...@unibo.it <mailto:aldo.g...@unibo.it>
> https://www.unibo.it/sitoweb/aldo.gangemi
>
>
>
> Director
>
> Institute for Cognitive Sciences and Technology,
>
> National Research Council (ISTC-CNR)
>
>
>
> http://scholar.google.com/citations?user=-iVGcoAAAAAJ
>
> skype aldogangemi
>
> twitter: @aldogangemi
>
> orcid: http://orcid.org/0000-0001-5568-2684
>
>
>
>
>
>
>
> On 14 Sep 2021, at 13:12, Giancarlo Guizzardi <gguiz...@gmail.com
> <mailto:ontolog-foru...@googlegroups.com> .
> <https://groups.google.com/d/msgid/ontolog-forum/5de3b00f56c941d0b54a46131284977c%40bestweb.net?utm_medium=email&utm_source=footer>
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Giancarlo Guizzardi

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Sep 17, 2021, 5:14:13 AM (4 days ago) Sep 17
to ontolo...@googlegroups.com
On Fri, Sep 17, 2021 at 5:24 AM doug foxvog <do...@foxvog.org> wrote:
On Wed, September 15, 2021 04:17, Giancarlo Guizzardi wrote:
> Hi William,
>
> What I meant to say with that passage is the following.
>
> 1) yes, there are multiple ontological cuts that can be made to reality.
> For example, a four-dimensionalist such as Chris would
> believe that not only John&Mary's marriage but also John and Mary are
> events. Someone holding my views, in contrast, will
> see John, Mary, and John&Mary's Marriage as endurants to which there are
> events associated that will constitute John's Life, Mary's Life,
> John&Mary's Marriage's Life (actually, to each of these endurants, there
> are associated multiple possible lives but that is a different story -
> see ).

Note that if one can reify both events and endurants, then both of you can
reify the same objects: John, Mary, John&Mary'sMarriage, John'sLife,
Mary'sLife, John&Mary'sMarriage'sLife.

The point is that a fourdimensionalist would have that
John = John's life, Mary = Mary's life and John&Mary'sMarriage = John&Mary'sMarriage'sLife
 

One then defines these objects as instances of the same classes: Person,
Marriage, Person'sLife, Marriage'sLife.  These can be agreed to be
subclasses of the same superclasses: Animal, Agreement, Animal'sLife,
Agreement'sLife.  At some higher level, the ontologies would separate into
whether things are events or endurants (if desired).

> 2) What I mentioned that both Chris and I would hold is the view that
> things like John, Mary and John&Mary's Marriage are things
> that really exist in the world. So, the piece of language "John&Mary's
> Marriage" picks up something really out there. Again, for Chris,
> this would be an event; for me, this can polysemically refer to both the
> endurant binding them and one of its possible lives (an event).

This is no problem.  It does not have to force itself at the level of the
individual or the immediate classes that each individual is an instance
of.


If I understand correctly what you mean then all of these reinforce your main point, i.e.,
that one can define these classification and identity relations
a posteriori. Yes. However, in my view, Endurants and Perdurants (events, occurrences)
and very different in nature, and from a modeling perspective,
knowing that beforehand is central to the approach

best,
Giancarlo
 

Giancarlo Guizzardi

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Sep 17, 2021, 5:38:15 AM (4 days ago) Sep 17
to ontolo...@googlegroups.com
On Fri, Sep 17, 2021 at 6:43 AM doug foxvog <do...@foxvog.org> wrote:
On Tue, September 14, 2021 16:38, William Frank wrote:
> Thanks, Giancarlo
>
> I found this very helpful:
>
>> Now, what makes something like a marriage a true endurant is that it has
>> essence and acciden