Views on when to use n-ary relations greater than binary - knowledge representation
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Robert Rovetto
Sep 10, 2021, 2:28:50 AM9/10/21
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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
Sep 10, 2021, 5:43:21 AM9/10/21
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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
Sep 10, 2021, 12:38:36 PM9/10/21
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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
Sep 10, 2021, 2:48:01 PM9/10/21
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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
Sep 10, 2021, 4:42:38 PM9/10/21
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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
Sep 11, 2021, 3:59:42 AM9/11/21
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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
Sep 11, 2021, 4:37:36 PM9/11/21
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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
Sent: Friday, September 10, 2021 4:43 PM
Sheth, Amit
Sep 11, 2021, 7:08:24 PM9/11/21
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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.
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
Sep 13, 2021, 1:59:08 AM9/13/21
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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
>
>
>
>
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
>
>
>
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Alex Shkotin
Sep 13, 2021, 5:06:06 AM9/13/21
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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
Sep 13, 2021, 5:24:25 AM9/13/21
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Well, at least now I know why the Web is making people stupider day by day …
Regards,
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Alex Shkotin
Sep 13, 2021, 7:25:38 AM9/13/21
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:-)
пн, 13 сент. 2021 г. в 12:24, Jon Awbrey <jaw...@att.net>:
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Jon Awbrey
Sep 13, 2021, 8:48:46 AM9/13/21
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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
>>> *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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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
>>>
>>> *-*
>>> OntologPage <https://ontologforum.org/index.php/RobertRovetto>
>>> IAOA Education Committee
>>> Contact <https://ontospace.wordpress.com/contact/>
>>>
William Frank
Sep 13, 2021, 10:24:43 AM9/13/21
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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
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sowa @bestweb.net
Sep 14, 2021, 12:01:28 AM9/14/21
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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.
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
Sep 14, 2021, 6:02:39 AM9/14/21
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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>:
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Alex Shkotin
Sep 14, 2021, 6:30:47 AM9/14/21
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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:"
- 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, entitybooks.example.comand the bookLenny_the_Lionparticipate. 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
Sep 14, 2021, 7:13:03 AM9/14/21
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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
Sep 14, 2021, 7:35:41 AM9/14/21
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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
________________________________
Aldo Gangemi
Full professor
University of Bologna
University of Bologna
Director
Institute for Cognitive Sciences and Technology,
National Research Council (ISTC-CNR)
skype aldogangemi
twitter: @aldogangemi
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dr.matt...@gmail.com
Sep 14, 2021, 8:45:45 AM9/14/21
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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
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Giancarlo Guizzardi
Sep 14, 2021, 9:31:41 AM9/14/21
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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
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Chris Partridge
Sep 14, 2021, 1:02:33 PM9/14/21
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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
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Giancarlo Guizzardi
Sep 14, 2021, 1:23:28 PM9/14/21
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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
Sep 14, 2021, 2:54:36 PM9/14/21
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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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