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. 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.).
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
R(a b c ... n)
to
(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. You must then have a way
of reconstructing the original situation by re-introducing the correct
logico-semantic relationships among the different entities. 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.
Pat Hayes
[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)?
Best regards,
GPZ
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