[Attempto] Object Ops, eq vs exactly?

[Norbert E. Fuchs]

On 30 Mar 2009, at 00:33, Joshua TAYLOR wrote:

> I notice that in the ACE DRS, the Op of an Object is "One of
> {eq,geq,greater,exactly,na}. eq stands for ``equal'' and geq for
> ``greater or equal''."

There are also "at most" (leq) and "less than" (less) that in the  
public version of ACE/APE do not occur in the object/6 condition, but  
in a quantity/3 condition to enforce the scope associated with these  
operators. See below for how this will be done in the next version of  
APE.

> What's the different between "eq" and
> "exactly"?  I can write ACE text that generates DRS with each of
> those, but I don't know if there's a difference in meaning.  The first
> two of the following three examples produce "eq,1", and the third
> "exactly,1".

We interpret "exactly N" as "leq N & geq N".

This leads, for example in RACE, to the following behaviour.

A man has 5 apples. |- A man has 4 apples.

A man has exactly 5 apples. |/- A man has 4 apples.

You can try this using the RACE web-client.

> ...

The next version of APE uses a modified representation of "at  
most" (leq), "less than" (less) and "exactly" (exactly) that uniformly  
takes care of the scopes associated with these 3 generalised  
quantifiers.

What is this scope?

While the deduction

A man has more than 5 green apples. |- A man has more than 5 apples.

is correct

A man has less than 5 green apples. |- A man has less than 5 apples.

is not correct since for "less than" (and similarly for "at most" and  
"exactly") you have to take the modifier "green" into account. We say  
that "green" is in the scope of "less than".

To express the scope the next version of APE uses a list notation.  
Here are the above examples in the new representation.

While the sentence

A man has more than 5 green apples.

generates the same DRS as before since "more than" does not have a scope

[A, B, C]
object(A, man, countable, na, eq, 1)-1/2
object(B, apple, countable, na, greater, 5)-1/8
property(B, green, pos)-1/7
predicate(C, have, A, B)-1/3

the sentence

A man has less than 5 green apples.

generates a DRS with a scope

[A, B, C]
object(A, man, countable, na, eq, 1)-1/2
    object(B, apple, countable, na, less, 5)-1/8
    property(B, green, pos)-1/7
    predicate(C, have, A, B)-1/3

indicated in this pretty-printed DRS by indentation. In the respective  
Prolog term the three conditions "object(B, apple, countable, na,  
less, 5), property(B, green, pos), predicate(C, have, A, B)" occur in  
a list.

The public version of RACE makes already use of this new scope  
representation.

By the way, indices like "1/8" are the new token IDs that stand for  
"sentence number/number of token within this sentence".

Regards.

    --- nef