You wrote:
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Also, it helps if you don't have to translate the binary relations themselves into case-based form:
r(a b)
is a lot more compact than
(exists (x)(r(x) & FirstArg(x, a) & SecondArg(x, b) ))
Pat
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Yuck! What a mess. DB folk sometimes
talk about a “Columnar” database as the flip side of the usual row
database. Instead of organizing tables (classes) with rows (instances), it
contains a set of columns and entities. Some columns are associated with some
entities in a way that can be uniquely identified – key column-entity
objects.
I wonder how a columnar database might be organized
for representing an ontology.
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
(949) 525-5712
725 Center Street
Costa
Mesa, CA 92627
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Monday, February 09, 2009
2:28 PM
To: Gian Piero Zarri
Cc:
gian-piero.zarri@xxxxxxxxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] New
Book: "Narrative Information"
On Feb 9, 2009, at 2:46 PM, Gian Piero Zarri wrote:
Dear Pat,
Pat Hayes a écrit :
On Feb 7, 2009, at 3:24 PM, Gian Piero Zarri wrote:
Dear All,
With respect to the recent discussion about "binary/n-ary", this
problem is dealt with in some depth in my recent "Narrative" book
introduced below (pp. 14-22). Very in short, we all agree about the possibility
of splitting n-ary structures into sets of binary structures.
Good, as this is a theorem :-)
However, this formal separation does not alter at all the original
n-ary character of a simple situation like "John gives a book to
Mary".
What do you mean by the "n-ary character"? Remember that n
here is a free parameter. Do you mean, in this example, the 3-ary character
(John, book, Mary)? Because, as Strawson argued convincingly many years ago,
one of the basic problems of thinking of these as multi-argument relations is
precisely that they have no fixed number of arguments. One can go an adding
qualifications almost for ever: John gave a book to Mary .. with pleasure, quickly,
in the evening, last year, in Geneva,
... and so on. (Strawson's example was: "He did it at mIdnight, in the
kitchen, with a knife, silently... " He made a sandwich, it turned
out.) If these have to be n-ary relations, then they are not n-ary for
any fixed n. They have to be variadic relations; but even that is not enough,
because any of the 'arguments' may be missing. Suppose we decide that the order
of the arguments of the relation is: subject, object, indirect-object, manner,
time, place, ... then we can handle your JohnBookMary example by the convention
(used for example in Common Logic) that the arguments are given from left to
right. But if we say "John gave it to Mary last year", without
specifying the "it", then the arguments which need to be filled in
are the subject, indirect-object and time, numbers 1, 3 and 5 in our argument
ordering. How can this be expressed as a conventional n-ary relation?
[GPZ] Exactly. To
represent in full this example without any loss of meaning we need, as you say,
a way of differentiating the arguments of the predicate GIVE by separating the
SUBJECT of the action from the OBJECT and the BENEFICIARY.
OK, after sending my response email in this thread, I looked at the way
your book suggests handling such examples, and we seem to be in violent
agreement. Your system uses a case-based description, just as most
linguistically oriented systems go, and for the very same reasons. So you are
already doing this.
BUt now I am puzzled by your claim that there is something inherently
wrong with the "reduction" to binary case-role descriptions, when
your own book describes exactly this approach. You seem to be attacking
yourself.
Doing this with explicit "roles" or, like you suggest, using
the convention that "... the arguments are given from left to right"
or by identifying these arguments with numbers do not change at all the core of
the problem: you are unable to recover fully the original meaning making use
only of your bag of binary relationships between GIVE and John, GIVE and book
and GIVE and Mary (or John and Mary etc.).
What part of the 'original meaning' is unavailable for recovery? The
binary case-role form asserts that an event in the category called
"give" - that is, a giving event - exists, in which John was the
agent - the giver - the book was the thing given, and Mary was the
recipient. This seems like a pretty comprehensive account of the meaning of the
sentence "John gave the book to Mary". What other part of this
hypothetical 'original' meaning needs to be REconstituted here?
I don't see that there is any problem here to solve. And if there is,
your own system has the same problem.
To infer something of interesting about this situation, we are then
obliged to "stick back" together, in some way, the elements of our
bag of binary entities in order to reconstruct the original n-ary unity.
This is already done in the binary form itself. The translation from
n-ary to binary proceeds by mapping
(exists (x)(R(x) & case1(x,a) & case2(x,b) 7 ... & casen(x,
n) ))
where the existential variable provides exactly the 'binding'
needed to provide the unity, and the original relation has become a classifying
property of this event-like thing that is asserted to exist. In real life one
typically uses more intuitive names for the binary relations, such as
(exists (x)(Giving(x) & Actor(x, John) & object(x, book) &
recipient(x, Mary) ))
[GPZ] Exactly, see
pp. 16-17 of my book.
Well, OK, but this transcription style is a standard going back over
many years. RuleML uses it, for example, as do several Prolog systems. It is
part of the folklore now.
You must then have a way of reconstructing the original situation by
re-introducing the correct logico-semantic relationships among the different
entities.
The 'x' in the above logical IS the 'situation'. If all you have is
your example sentence, there is nothing more to re-introduce. If you have more,
eg the sequence:
John gave the book to Mary. It happened last year, in Marienbad.
then the logical form of the information will be more complicated:
(exists (x)(Giving(x) & Actor(x, John) & object(x, book) &
recipient(x, Mary) & where(x, Marienbad) & when(x, 2008) ))
I still fail to see what you mean by RE-constructing anything.
Note that I don't contest at all the practical utility of splitting
n-ary relations into sets of binary ones - for example, for efficiency's sake
when storing knowledge into permanent memory.
The (binary) W3C languages are unable to do this
On the contrary, this is exactly what they do. In the RDF-style
notation, the 'x' here is an RDF blank node.
: this is why they are not very useful for dealing correctly with
situations characterized by a minimum amount of semantic complexity - and this
too is very well known.
Sorry, but this is tendentious nonsense. The binary form sketched above
has many, many advantages over treating event or situation descriptions as
multi-adic relationships. So many, in fact, that it has become a standard in
linguistics (almost universally) and many applied rule systems. The most
obvious is that it provides an explicit name for the event or situation itself,
thereby allowing it to be described and related to others. The relational form
does not imply that anything exists,
a grave ontological weakness.
[GPZ] If RDF/OWL were
really able to deal with n-ary situations, how can you explain that well-known
exponents of the W3C world have spent at least two years trying (with very poor
results) to extend these languages in order to represent n-ary relationships
(see http://www.w3.org/TR/2006/NOTE-swbp-n-aryRelations-20060412)?
Because the case-based translation isn't ideal for all purposes, and
some people want to directly use n-ary relations for n>2, for other reasons,
some of which are outlined in the note you cite. (Which I would add is just one
note, and shouldn't be said to be definitive; and does not in any case describe
a language extension.)
Also, it helps if you don't have to translate the binary relations themselves into case-based form:
is a lot more compact than
(exists (x)(r(x) & FirstArg(x, a) & SecondArg(x, b) ))
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