[Attempto] Meaning of the copula "to be"

[Norbert E. Fuchs]

On 19 Apr 2012, at 16:58 , shruti sugunan wrote:

> Im trying to work with RACE.
> I tried this,
> 
> AXIOMS:
> A node is a title.It depends on some colors.
> 
> QUERY:
> What is a node?
> 
> 
> THIS IS THE ERROR I AM GETTING:
> Query cannot be answered from axioms.
> 
> I CANT UNDERSTAND WHY WOULD SUCH A SIMPLE QUERY NOT WORK?



On 19 Apr 2012, at 22:43 , Norbert E. Fuchs wrote:

> That RACE does not answer your query is related to what I wrote in my preceding message to George Henson, namely that the current version of RACE does not allow the deduction
> 
> (1) A node is a title. |- A title is a node.
> 
> Thus when you try
> 
> (2) A node is a title. |- What is a node?
> 
> you implicitly assume (1) to match " What is a node?". 
> 
> With the current restriction of not allowing (1) RACE will, however, answer the query "A node is what?".
> 
> I'd be interested in the feedback, yours and those of the other contributors, whether or not (1) should be reactivated.

Hi

I'd like to come back to your axiom

A node is a title.

since I am wondering what you wanted to say. Should your sentence mean

(3) Every node is a title.

or 

(4) There is a node that is a title.

Let's assume that you meant (3)
-------------------------------
The copula "is" has the unambiguous meaning "is subclass". (3) expresses that the class "node" is a subclass of the class "title".  

A side remark: in this case the pronoun "it" of your second axiom "It depends on some colors." cannot be resolved since "Every node is a title." does not export any antecedent. You would have to say "Every node is a title that depends on some colors."

The deduction 

Every node is a title that depends on some colors. |- What is a node?

will fail since the universally quantified axiom does not introduce any node.


Let's assume that you meant (4)
-------------------------------
(4) is ambiguous between between the readings 

(4a) There is a node that is an element of the class title.

or the reading 

(4b) There is a title. There is a node that is the title.

where (4b) should express the equality of "title" and "node". To make the equality available for reasoning you need to introduce the three axioms that make equality an equivalence relation

(reflexivity)    |- A is A.
(symmetry)       A is B. |- B is A.
(transitivity)   {A is B., B is C.} |- A is C.

Thus if these three axioms are available, then (4) is interpreted as (4b) expressing the equality of "title" and "node". If these three axioms are not available, then (4) is interpreted as (4a).

In the current public version of RACE the three equivalence axioms are not available – they are deactivated – and (4) is interpreted as (4a) "There is a node that is an element of the class title."

Consequently, the deduction

(2) A node is a title. |- What is a node?

fails, and the deduction

(2') A node is a title. |- A node is what?

succeeds. If RACE would use the three equivalence axioms then both (2) and (2') would succeed.

As I wrote in my previous message, I would appreciate your feedback whether RACE should use the three axioms that make the copula an equivalence relation in cases like (4).

Regards. 

Norbert E. Fuchs
Department of Informatics & Institute of Computational Linguistics
University of Zurich