attitudes to Krep
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Date: Mon, 22 Nov 1993 14:46:47 +0000
To: interlingua@ISI.EDU
Subject: attitudes to Krep

I think I am beginning to understand two different perspectives on Krep
that Fritz and I exemplify. This might be of wider interest than questions
of what order one likes ones logic to be.

Suppose someone produces a formalism of some kind and claims that they have
an account of what it means. What justifies such a claim? 

One view regards the Krep process as simply part of logic and mathematics,
the use of formalisms by humans to express things. On this view, no
justification, other than simple technical competence, is needed: 

>When Joe KR-User declares simply that "All monotonic functions of 42 have
>>positive values" he means it ...

This is the perspective which assumes that we begin with agents (we
Joe-users) who know what we mean and have intentional status, and the
business of Krep is simply to aid their communication. So if one agent
simply *declares* that he means 'is-very-big' to mean being very big, he
has a perfect authority to assert this, and is under no obligation to
provide any kind of computational justification for such a claim:

> The fact that we may not be able to compute all of them in 
>finite time is irrelevant -- and  the fact that functions like 
>Pat's concept "VERY BIG" are included is also no problem....

This view has an attractive robustness when applied to issues in the
philosophy of mathematics. Meanings are already there, people mean things,
and they use formalisms to say them. We all know what 'finite ' means, and
we can prove that it isnt computationally capturable: but thats OK, since
if we declare that "f17" means finite, then thats what it means.

On another view, what we are trying to do in Krep is formalise the
knowledge used by a computational agent. On this view, our long-term aim is
to analyse the architecture of a cognitive agent, and the K in Krep is
ultimately going to be part of such an agent. On this persective, questions
of what makes the knowledge actually have meaning - questions that the
first view regards as trivial - become central (and indeed are the topic of
extended and heated intellectual debate). We cannot appeal to the
intentions of 'Joe KR-User' because he is just the programmer who
implements the artificial cognitive agent, and the issue is what that agent
itself can be said to mean by its represented knowledge. Or to put it more
anthropocentrically, if we hypothesise that people work (in part) by
manipulating mental representations, how do these representations get their
meanings? How are they 'grounded'? An account of meanings in Krep, on this
view, has to somehow explain how computational manipulations of
representations are related to their intended meanings, which is not at all
easy to do. On this perspective, for a human to simply *claim* that some
symbols in a robot denote all monotonic functions of 42 is an empty boast.
And showing that a semantic claim can never correspond to anything
computable renders it vacuous.

In the email discussion I have been arguing from the second perspective,
assuming that Krep is part of AI and the aim of AI is intelligence, or at
least cognition.  Fritz has been arguing, I think, from the first, in which
Krep is a computational extension of conventional logic and mathematics, on
a par with CAD. Neither of us is wrong, but we need to get our assumptions

If the role of Krep systems is essentially to communicate between human
users, then I agree that completeness is a purely technical matter of
relatively little importance. We can agree that "A" means "Start the engine
in five minutes", and then use KIF to send "A" as correctly as morse
signals or naval flags. If it is supposed to be *used* by the computer as a
representation, however, then its computational properties become more
significant, and completeness of a proposed semantics becomes a matter of
more importance. If its computational use is all there is, then any claims
for what it means must involve giving an account of how the machine's use
of the formalism somehow corresponds to the meaning it is said (by Joe-User
or anyone else) to have. And that correspondence is a completeness result.

Pat Hayes

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