Pat, Gian Piero, and Rich, (01)
We all seem to agree that a triadic relation, such as give(x,y,z), can
be mapped to and from a linguistic representation that uses an entity
of type Giving (or whatever you want to call it) and three binary
relations. Following is an equivalence stated in CLIF: (02)
(forall (x y z)
(iff (Give x y z)
(exists (w) (and ((Giving w) (Agnt w x) (Benf w y) (Theme w z))))) (03)
The points of contention are (04)
1. Is one form preferable to the other? Which one? Why? (05)
2. Does one form lose information contained in the other? (06)
3. Do verbs such as 'give' have a fixed arity or should the
number of possible arguments be considered open-ended. (07)
For #1, it seems obvious that (Give x y z) is more compact than the
expansion. If all other things are equal, a more compact form is
usually more efficient than a more expansive form. The people who
implement "triple stores" claim that they can handle the expanded
form with purely binary relations more efficiently than a form with
n-ary relations for arbitrary n. But others who process very large
graphs have developed efficient ways of handling n-ary relations. (08)
The linguists have a stronger argument for the expanded form:
it explicitly shows linguistic information that is important
in translations to and from natural languages. They can state
a small number of general rules for handling each type of
case or thematic relation instead of writing a much larger
number of specialized rules for each type of verb. (09)
For #2, the answer is "Yes, but." (010)
The compact form loses information about the thematic roles,
and the expanded form loses information about the connectivity.
*BUT* any information lost by the transformation is contained
in the equivalence rule that states the transformation. (011)
So the debate centers around how easy it is to find the
transformation rule when needed and apply it to recover
whatever information was lost. (012)
For #3, Pat cited an argument by Strawson: (013)
PH> 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.) (014)
Long before Strawson, linguists had observed a distinction between
obligatory and optional (AKA inner and outer) participants in the
action or state expressed by a verb. For 'give', the number of
inner or obligatory participants is 3, and there is an open-ended
number of optional relationships for the time, place, manner, etc. (015)
For this reason, it is often useful to distinguish the two kinds
of relations. One way is to bind three of them into a triadic
'give' relation, and bind the others to a situation that contains
the act of giving. Another way is to assign a higher priority
to the obligatory or inner relations. (016)
PH> 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. (017)
A typical example is Between(x,y,z). (018)
John (019)
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