[Attempto] Meaning of the copula "to be"

[David Whitten]

Norbert,
thank you for the excellent explanation. One of the reasons I joined the
attempto
mailing list is because I hoped to have these kinds of conversations.

This is what I think I understand.
If you don't make "is" an equivalence relation, then
with a sentence like:

a tonsure is a pate.

You know these things are true:
There is a classification of some things named "tonsure".
There may or may not be any thing that can be classified as a tonsure.
No example of a tonsure is currently known in this axiom set.
There is a classification of some things named "pate".
There may or may not be any thing that can be classified as a pate.
No example of a pate is currently known in this axiom set.
If there was some thing X that could be classified as a tonsure
then that same thing X must also be classified as a pate.

What you don't know is:
If there was some thing X that could be classified as a pate
then that same thing X could also be classified as a tonsure
or may not be classified as a tonsure.

If we made "is" into an equivalence relation, then I think we don't
get the second behavior from RACE.

Let us add the statement to our axiom set of

A pate is a scalp.

Given that Pate (the capitalized word) means the set of all things
classified as a pate.
Given that Tonsure (the capitalized word) means the set of all things
classified as a tonsure.
Given that Scalp (the capitalized word) means the set of all things
classified as a scalp.

If "is" becomes an equivalence relation, and substituting into your example
below,
we would get

(reflexivity)    |- Tonsure is Tonsure.
(symmetry)       Tonsure is Pate. |- Pate is Tonsure.
(transitivity)   {Tonsure is Pate., Pate is Scalp.} |- Tonsure is Scalp.

By the way, for an equivalence relation I think these are true as well:
(reflexivity)    |- Pate is Pate.
(reflexivity)    |- Scalp is Scalp.


I agree that all of the reflexivity statements are true,
I don't agree that the symmetry statement is true
I do agree that if "a pate is a scalp" were true then the
transitivity statement would be true.

Unfortunately for my example,  a tonsure is a scalp, but
a pate includes both the scalp and the hair on the crown of the head,
and so "pate" refers to more than "scalp" does.

SInce I purposely used obscure words, these are the meanings that I intend.
By the way, a pate isn't the same thing as a* **pâté**, which is a food
made of liver meat.**
*The word  "pate" is an archaic word from before the 1370's and
means the  head of a person. It is far more common to call this the crown
of the head in modern times.  Personally, I have only heard the word "pate"
referring to a human's head, but according to one website,
Noah Webster's dictionary in 1828  also used "pate" to refer to the head of
a calf.
A tonsure is a shaved pate.  When a person joins certain groups,
notably to be a monk, the crown of the head of the person is shaved.
A scalp is the skin of the crown of the head, and may or may not be shaved.

So my vote is that we don't make "is" an equivalence relation.
What kind of relation is it if we drop the symmetry requirement?

David
PS: I would also like to discuss how "part of" interacts with "is"
perhaps in a different email thread.  As I was discussing this
ideas about merology came up with my example.
"the pate of the head", "the crown of the head", the "scalp of the pate",
"the tonsure of the crown",  are some examples that I would like
to know about how RACE handles conclusions.

Could we have a "wordy" RACE mode where the statements that
come from how "is" is classified as a relation would be explicitly
stated? I'm thinking these should include the reflexivity, symmetry,
and transitivity facts if they are used in concluding some result,
to help a someone who hasn't used RACE before understand
the conclusions RACE draws?  I know they aren't currently used
by "is", but are they used by the translation of other English words
into the DRS form?

On Fri, Apr 20, 2012 at 7:27 AM, Norbert E. Fuchs <fuchs at ifi.uzh.ch> wrote:

>
> 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
>
>
>
>
>
>
>
>
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