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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "doug foxvog" <doug@xxxxxxxxxx>
Date: Wed, 9 Nov 2011 14:32:09 -0500 (EST)
Message-id: <64692.>
On Wed, November 9, 2011 10:47, John F. Sowa said:
> ...
> EB (Ed Barkmeyer)
>> In my experience, there are intrinsically ternary and quatenary verb
>> concepts.    (01)

There is a distinction between intrinsic arity of verbs and the form
in which languages express them.    (02)

However, I read this discussion not as one about the features of
languages, but about ontology.  I think your main meaning is that the
things that verb represent (events and situations) may intrinsically
have two, three, or four relations that are necessary for sufficiently
describing them, irrespective of the language (formal or natural) used
to make statements about these events and situations.    (03)

E.g., a Giving event must have a provider, recipient, and thing given,
while a Selling/Buying event must have a seller, buyer, thing sold, and
final sales price.  Similarly, it is intrinsic that a marriage have two
spouses.    (04)

It may just be a matter of terminology, but i'm not sure of the utility
of stating that a class of objects has a certain arity just because
it would take a relation of that arity to fill all the key binary
relations for that class of objects in a single statement.  It strikes
me as likely to cause confusion between an instance of such an object
and a statement using the n-ary relation that partially defines the
object.    (05)

I do find it ironic that in the examples of Giving and Buying, that
although Buying can be represented as an exchange of two Giving events,
that one of the intrinsic slots of the monetary Giving event is not
intrinsic in the Buying event.  In the Buying event, the monetary value
of the amount tendered is considered intrinsic, while the tender object
-- the thing given -- is not.    (06)

>> English grammar supports [intrinsically higher ordered verb
>> concepts] with the use of prepositional phrases,
>> but listeners use those prepositional phrases in comprehending
>> the verb concept.    (07)

Or other linguistic structures, such as John's example using indirect
objects.    (08)

> JS
> That's true for verbs like buy and sell, which have 4 slots:    (09)

>     Sam bought the book from Bob for $10.
>     Bob sold him the book for $10.    (010)

But also note:
      Sam bought Bob the book for $10.    (011)

This also uses 4 slots, three implicit in the language (S, DO, IDO) and
one with a prepositional phrase, but the 4 slots are different than
the 4 in the previous examples.  This suggests that the "intrinsic arity"
of verb concepts does not have to be features of the language.    (012)

Case structured languages do not need multiple verbs which other languages
use to order the slots.  Finnish, for example, does not distinguish lend
and borrow.  The case markers distinguish the provider and the recipient.    (013)

It is useful to describe necessary relations which must hold for the event
or situation types that are described by verbs.  However, natural language
normally provides ways to partially define the situation even if all the
"necessary" information is not provided (or known).    (014)

Some of the "necessary" slots might not be interesting for the purposes
of the communication or the data storage:    (015)

    I bought potatoes at the farmers' market.
         (who cares from which vendor)
    Farmer Brown sold all the potatoes she brought to the market.
         (who cares which shoppers purchased which potatoes)    (016)

> But English also has ditransitive verbs that have 3 slots:    (017)

>     Mary painted the wall yellow.
>     Sue gave the child a present.
>     Bill considered her generous.    (018)

The DO could be omitted from the first case; it could not in the second;
and doing so in the third case alters the meaning:    (019)

     Mary painted the wall.
     Sue gave the child. *
     Bill considered her. ?    (020)

Is the color that something was painted part of the "intrinsic arity"
of the concept of painting?  What about the paint texture?  ... whether
it was enamel, oil, latex, watercolor, or some other variety of paint?
... how may coats were used in the painting?  ... how the surface was
treated before painting?  Etc.    (021)

Certainly, various things must be true in order for a situation/event
of a specified type to happen and are meaningful to express.
For every situation and event, the timing of the event is meaningful.
For every event, the change of state, is meaningful.
For every action, the performer of the action is meaningful.
For every transfer, the transferred thing is meaningful.
For every change in user rights (a type of transfer), a to possessor
and/or a from possessor are meaningful, and the transferred thing
is something to which user rights have changed.    (022)

For every giving, the recipient and the thing given are meaningful; the
performer of the action is the giver.  If the thing given is a (physical
or abstract) object the giving event is also a transfer of user rights,
but it isn't if the thing given were an action (such as a smile, a
massage, or the repair of a dent).    (023)

A selling event includes a change in user rights to some medium of exchange
in exchange for some giving event.  Thus the roles of both giving events
and changing user rights are meaningful.  The buyer of the selling event
is the giver of the giving of medium of exchange event and the recipient
of the thing purchased.    (024)

[Note that buyer, seller, and even thing purchased slots can be
 split upon detailed analysis.  We can distinguish various buyer
 slots when a person makes a corporate purchase.  We can distinguish
 various seller slots when an employee of a consignment shop sells
 consigned goods.  Multiple thing purchased slots could distinguish
 among a ticket, the right to view the play, and the experience of
 viewing the play.  And wouldn't the credit card, the credit card slip,
 and the bank transfer all have different medium of exchange slots?]    (025)

> EB
>> My point is that we must first distinguish between n-ary database
>> relations, which may represent compound statements or relations with
>> adverbial modifiers, and conceptually n-ary relations.    (026)

Agreed.  In a given database line, there may be multiple binary relations
expressed between various column fillers, while other groups of column
fillers must be grouped because they each provide information about
some other thing (an event, account, ...) which bears a relation to
the focal thing represented in the column.  For example, a single
database line might have a set of columns about the purchaser in
a sale, another set about the shipper, a set about the place for
delivery, a set about the item(s) purchased and shipped, and another
set about the state of the shipment at various points in time.    (027)

Such groupings determine what could be expressed with n-ary relations,
but, so long as the ancillary objects are reified, do not require that
n-ary relations be used.    (028)

Intrinsically n-ary relations would include ordering and betweenness
relations as well as ones in which one argument restricts another,
for instance by amount
or some other modifier
   (appropriateAttireForRolePlayerInType ATTIRE SITUATION-TYPE ROLE)
in which there seems no use in creating a subclass from the modifier
and the thing modified.    (029)

> Yes.  Many relations are constructed by joining two or more
> relations with fewer arguments.  ...    (030)

>...  There are often very good reasons for defining "views" that
> add arguments by joins or delete arguments by projections.
> ...    (031)

> John    (032)

doug foxvog    doug@xxxxxxxxxx   http://ProgressiveAustin.org    (033)

"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.
=============================================================    (034)

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