Pat, Gian Piero, and Rich,

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:

(forall (x y z)

(iff (Give x y z)

(exists (w) (and ((Giving w) (Agnt w x) (Benf w y) (Theme w z)))))

The points of contention are

1. Is one form preferable to the other? Which one? Why?

2. Does one form lose information contained in the other?

3. Do verbs such as 'give' have a fixed arity or should the

number of possible arguments be considered open-ended.

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.

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.

For #2, the answer is "Yes, but."

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.

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.

For #3, Pat cited an argument by Strawson:

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.)

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.