Re: attitudes to Krep
Date: Fri, 03 Dec 1993 10:07:18 -0400 (EDT)
Subject: Re: attitudes to Krep
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Dear Pat Hayes,

	Your last message (which I just cc'd to and correctly set out the

> two different perspectives on Krep that Fritz and I exemplify.

Quite right, but, whoa, not necessarily "two different perspectives on
Krep", just on knowledge interchange!  I take the phrase "Knowledge
Interchange Format" at face value, and I support KIF for interchange
but I wouldn't consider it as the "definiens" of the internal meaning
of knowledge in AI.  As Tom Gruber aptly put it,

|This work falls in the pragmatic side
|of Pat Hayes' dichotomy: i.e., the purpose of the ontology is to
|facilitate communication and not to prescribe the cognitive
|structures of the agents.

	Conceptual Graphs theory is more (it has more ambitious
notions of canonicity of complex concepts, procedural actors, and
a base-level of conceptualized "case"-like relations, among other
things) but the more limited, pragmatic view of knowledge
interchange semantics also applies to the "KIFian" part of CGs.

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

	Briefly: nothing ultimately but A. Compositional structure,
and B. Ostensive pointing to something (a shared basic experience). 
The really interesting question is: how much of the universe is in
A (almost none? almost all?), and how much requires a bit of B. 
It's a matter of degree.  As I said before, when logicians explain
AND and NOT as primitives (or, more obnoxiously, use 42
applications of SUCCESSOR or set-brackets to supposedly "define"
essential 42-ness), even they do a bit of B.  In my view,
compositional structure is precisely that which both man and
machine can genuinely "experience in common", and relational
(hyper) graph theory alone is inherently "grounded" for both.  This
is just the "network" part of a semantic network.  We shouldn't
pursue this topic here, though.  It's not the job of a Knowledge
Interchange language to settle the unsettled philosophical
questions in AI like symbol-grounding; in fact its job is exactly
the opposite: to serve all camps.

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

	You dismiss this position with the example:
>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.

	For "finite" this lampooning applies only to devotees of
First-Order-ism.  The classical (i.e. n-order) logicians around
the world (like non-logicians) think they know what "finite" means
-- they have a second-order definition which is not of the "f17"
ilk.  Only First-Order-ites seem to have the problem.  The same is
true, I gather, for connectedness of finite structures, planarity
of same, beta-reduction of lambda sentences, numbers, reals,
particular topological spaces, and all strongly-but-not-weakly-
higher-order-definable concepts.  It is the First-Order-ites who
would need to have these as primitive predicates, like "red" or
"f17", and relegate those predicates to a mechanism external to
the logic.  But, yes, I do mean to include some predicates in a
knowledge interchange language that have meaning only to people. 
Maybe only a few semantic primitives of this type are needed,

>... for a human to simply *claim* that some
>symbols in a robot denote all monotonic functions of 42 is an empty boast.

	Look, I KNOW that all monotonic functions of 42 have positive
values.  Is that an empty boast?  I'll bet you know it too.  It has
nothing to do with our ability to compute any of these functions,
or run over a bunch of values in some First-Order Tarskian model-
theoretic domain.  It follows from genuine, higher-order (or
"intensional") knowledge about "monotonic", "positive", "function",
etc.  So, unless you want to adhere to some theory of an
ineluctable, inherently unattainable transcending power of human
intelligence over machine intelligence (which I kinda' doubt), you
should let machines be able to know it too.  If First-Order-ism
precludes even expressing such ideas, then using it as the formal
semantic basis for a "universal" interchange language would hobble
the language.

>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. 

	The semantics in the second case should be sound, and the
computer's actions should _conform_ to the semantics (e.g. not
violate boundaries or structure-preserving conditions or disobey
the Galois connection) of all of the compositional operators in
the language, but typically there will be some capabilities
outside the formal semantics in the form of primitive non-logical
predicates with external criteria for meaning.  The criteria may
even be merely "operational".  Completeness in this sense is not
essential nor expected for a practical interchange language,
although it might be part of your grander vision of logically
formalizing the whole of an agent's semantics.

>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.

	I do not believe that "its computational use" will be "all
there is" for any likely application of a knowledge interchange
language.  I expect almost every application to interpret some of
the meanings of "computation" from outside the system.  Usually by
a human being, but even if only by means of a robot's physical

                         Yours truly, Fritz Lehmann
4282 Sandburg, Irvine, CA 92715 USA    714-733-0566