Re: Peirce's rules of inference

phayes@herodotus.cs.uiuc.edu
```Message-id: <9208281603.AA20839@herodotus.cs.uiuc.edu>
Date: Fri, 28 Aug 1992 11:05:41 -0600
To: sowa@watson.ibm.com
From: phayes@herodotus.cs.uiuc.edu
Subject: Re: Peirce's rules of inference
Cc: INTERLINGUA@ISI.EDU, SRKB@ISI.EDU, CG@CS.UMN.EDU
```
```
John,

I bow to your historical scholarship, which I never intended to challenge.
I agree that the Principia logic, like many non-N.D. logics, is quite awful
in use, and one of the main reasons is that its rules apply only at the
'top' level, so that to apply obvious inferences below that level, as in
your example, requires longwinded, artificial and unnatural processes of
unpacking and repacking. (As an aside, I also note that our university
system spends a fair fraction of its effort teaching undergraduates to
manipulate these artificial notations, cf. any logic textbook. I tried to
get Rochester to do something different and was suppressed: on asking why,
they told me it was good mental discipline to put the kids through. Like
Latin in England.)

However, that was not my main point, but to look more pragmatically at what
could be done on machines right now. And to return to 'contexts', I think
you are contributing to the confusion surrounding this term. You say that:

>I use the word "context" in a very narrow sense -- I mean it as nothing
>more than a notation for packaging a collection of graphs. ....  A [context]
>could contain all the world's knowledge or it could contain just one simple
>atom.

but a few lines later we get a shadow of the more exotic idea again:

> For such systems [CYC-ish], it is important
>to analyze the permissible operations for moving information in and
>out of various contexts (i.e. packages), reasoning within one of those
>packages, and then exporting an answer to another package.

But this notation doesn't preserve any structure whatever, as you have just
said: it gives complete freedom to move anything in and out of these
scope-contexts.

There is a claim here: that there is a significant idea of a 'context',
which is something which plays a nontrivial role in complex tasks of
large-scale knowledge representation. This idea, or rather collection of
ideas, is new and now being gradually got clear by McCarthy, Guha and
others. But its not a notational idea. It could probably be realised in
just about any logical notation you like. To identify these semantically
important CYC-contexts with Pierce's bracket-scopes (or anyone else's way
of indicating the scope of quantifiers or connectives) misses their point,
and if taken seriously is likely to be far too restrictive on our semantic
imagination.

But I expect we agree, really. Its hard to disagree with:

>a proof procedure that preserves the package structure can