Re: Roles, again (Pat Hayes)
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Date: Tue, 12 Sep 1995 14:07:39 -0600
To: (Bill Brayman),,,
From: (Pat Hayes)
Subject: Re: Roles, again
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At  1:56 PM 9/11/95 -0700, Bill Brayman wrote:
>Pat hayes replies:
>>What you are calling 'roles' here are simply the argument places of the
>>relation, and your conceptual Jabberwockiness comes directly from trying to
>>think of them as actual entities when they are, at best, only a kind of
>>metasyntactic relationship between a relation and a sort.
>Pat, time to break out of the 9 dots*. 

I know the puzzle and its solution. In response, I suggest it might be time
for you to leave the hall of mirrors.

> Meta (syntactic) to what? 

To the assertion that the relation holds between its arguments.

> I for
>one would like to see a logic system that covers "seller" or
>"buyer" (for example) as more than a syntactic relationship.  "Argument
>places" is a
>closed-world-assumption kind of concept. 

Ordinary logic makes no closed world assumption. I dont know what you are
talking about. Do you mean that you want to allow relations with an
indeterminate number of arguments? KIF allows this, and it seems to work
fine, although care is needed in matching. If you really want to give
labels to the argument positions, i guess you could, but don't think that
they are anything more than that.

Consider "seller". This might be considered a unary property of people:
someone is a seller if they sell something to someone for some amount. This
is easy to say:

seller = (lambda x)(exists y,z,u)(sells-to-for(x,y,z,u) & <appropriate
sortal conditions>)

similarly, buyer = (lambda x)(exists y,z,u)(sells-to-for(y,x,z,u) & ...)

What more do you need?

, and  I want a logic that allows me
>to reason without having to thread down to what I think you experts
>call the herbrand universe to determine the role of the arguments.
>Bring the role definition to the top. 

The arguments of a relation in a sorted logic are assigned sorts directly,
right at 'the top'. There's no threading down or Herbrand universe

>That's how humans reason.
I admire your bravado. Can you cite any experimental studies?


PS. Your puzzle is too easy:

. . . 
|\| |
. . .
| |\|
. . .

You should have also said, "without lifting the pen from the paper".Thats
when you get the puzzle with the 'breakout' answer.

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