Re: Responding to all those messages

sowa <>
Date: Mon, 10 May 93 07:43:43 EDT
From: sowa <>
Message-id: <>
To:, interlingua@ISI.EDU,
Subject: Re: Responding to all those messages

In a note responding to Len Schubert (after the note in which I responded
to several of your notes, I said that I found no disagreement with him (Len)
about any of the formal operations he was doing.  His comments supported
my contention that an intermediate computational level between the KR
language and the world was commonly used in AI systems.  In order to
avoid the loaded word "model", I suggested that we adopt Jerry Aronson's
term "ontological depiction" or more briefly just "depiction".  Using
that term, I suggest the following revision to my four-part distinction:

   Natural language <--> KR language <--> Depictions <--> World

These depictions are constructions implemented on a computer that
are very model-like:  they consist of individuals and relations (tuples)
over those individuals; there are no quantifiers, negations, or other
Boolean operators in them.  The individuals in the depictions are of
two kinds:

 1. Literals:  Numbers or character strings.

 2. Surrogates:  Lexical items used as unique identifiers for
    physical objects that cannot be stored inside the machine. 

Formally, I can think of the depictions as Tarskian-style models
of axioms stated in the KR language.  But you can, if you please,
consider them as a purely heuristic device for computing the
correspondence between the symbols in the KR language and the world.
If you choose to believe that models should be made of real world
objects, then you can do so.  But since my surrogates are in a 
one-to-one correspondence with your objects, there is no observable
difference between what you and I actually do -- all of our formal
operations are identical.

The advantage of depictions is that it gives us a formal level
that corresponds to actual practice in AI and other branches of
computer science.  They enable us to consider multiple depictions
of reality and multiple possibilities, but without mentioning
"possible worlds" with all their dubious metaphysical baggage.
Possible worlds believers can, if they wish, think of my depictions
as possible worlds (Lewis, in fact, calls them ersatz worlds).

Some comments on your comments:

> ... I don't
> think that databases are essentially different in kind from sets of
> assertions. Large, tedious, ground sets, to be sure, but semantically 
> in the same league. 

> The reason for this is not because its so easy to implement both in LISP, 
> by the way, but because if we look carefully at what databases are supposed 
> to mean, they seem to be semantically indistinguishable from a collection 
> of ground assertions (probably together with some closure assumptions). 

Yes, of course.  A model can be generated from a collection of ground
assertions, and a collection of ground assertions can be derived from
a model.  The two are isomorphic.  Therefore, I can call a database a
model, and you can call it a theory composed of nothing but ground
assertions.  There is no operational test that can distinguish what
we do.  Therefore, I propose the more neutral term "depiction" in order
to avoid using the word "model" or "theory".

> This is a perspective from which one can view languages like SQL, true. 
> One might also think of the question-answering process as being one of 
> making inferences, however, which I prefer to do. So viewed, questions 
> about the validity of the question-answering process, for example, 
> become meaningful. 

These are both valid ways of answering questions.  Syntactically, you
can answer a question by using rules of inference.  Semantically, you
can answer it by looking at a model.  If you think of your DB as a theory,
you are following rules of inference; if you think of it as a model, then
you are evaluating the denotation of a formula.

Comutationally, there is an important point to note:  theorem proving,
in general, is NP complete; but evaluating the denotation of a formula
in terms of a model is computable in polynomial time (with the number of
quantifiers in the formula as an upper bound on the exponent).  Most
DB systems take advantage of the model-like properties to improve
performance; by hashing and indexing, they can often reduce the time
even further.

> Also, I have to insist (again) that you are incorrect in implying that 
> Tarski's models - and certainly TMT models (if you like, those defined in 
> Scheonfeld's textbook) - need to be computable. Usually, denotations 
> can't be computed, nor should one expect them to be computed (with the 
> ordinary sense of 'compute'). 

I never said or implied that a model must be computable.  As a mathematician,
I am willing to consider noncomputable structures, and I am even willing
to talk about nonconstructive and uncountable structures (despite my
agnostic reservations about them).  But as a computer scientist,
I not only insist on things being computable, I insist that they be
computable in reasonable time -- preferably polynomial or better.

> ... I think I now understand why you 
> believe models are computable. Just stop insisting that they must be.

To repeat:  I never insisted that models must be computable for mathematics.
But I do insist that they must be computable for computer science, which
includes AI.  You can, if you wish, use KIF or CGs to state mathematical
theories that may have noncomputable or even uncountable models.  But
any such model is an abstract, mathematical object -- not a collection
of physical objects.

> Yes, but it implies something even stronger, viz. that the set-theoretic 
> constructions are computable. (Or do you not mean to imply this? Eg would 
> you call the set of all integers a datastructure? If so, then we simply have 
> been using language differently. Incidentally, your apparent identification 
> of 'mathematical construction' with 'datastructure' is one of the reasons 
> I accused you of confusion. Being a constructivist makes the identification 
> acceptable, and is less of a sin.)

I think this is where the misunderstanding has come in:  we have been
talking about many topics in mathematics, computer science, and AI.
I never claimed that all set-theoretic constructions are computable,
even though I would be happy to talk about them mathematically.  But
for computer science, only computable and preferably efficiently
computable structures are relevant.

> By the way, these intermediate 'models' seem more and more like mental 
> images if they have to be attached by robotic equipment to the World.

Yes, exactly.  Image processing is a very important part of robotics.
And those images must be related to both the KR languages and to the
mechanical manipulators.  That is why I like the term "depiction".
It suggests images, but I define it in a way that is nicely computable
and avoids questions about what goes on inside people's heads.

> Yes. Well, I disagree, and I challenge you to define 'image-like' in 
> a coherent way. But more to the point, even if I concede this, it 
> certainly should not entail that the validity of my inferential thinking 
> should be discussed in terms of such images.

A very large part of my _Conceptual Structures_ book was devoted to
this issue.  All of Ch. 2 was a survey of psychological evidence on
both sides.  But in any case, I never suggested in the book or in my
previous notes that "the validity" of inference depended on images.

> An important point here. While a database can be seen as a model, 
> as I am quite willing to admit, if it is used as a source of information 
> then it is not being TREATED as a model in the TMT sense. Suppose the database 
> has <salary Pat insufficient>. Can I conclude that Pat's salary is
> insufficient? 
> If so, then that dbase entry is being treated as an assertion. If it were 
> only one relation in a single TMT model - a single possible world - that 
> conclusion would not be valid, since another model of the salary theory 
> mightequally well have <salary Pat $10^6>.  A TMT model is not another 
> representation, but a way the world might be structured in order for 
> the representation to be correct.

I think that this is getting at one of the main reasons why I want to
have computable models (or depictions):  they are excellent sources of
information.  But in order to get that information out of the model,
we have to distinguish the language from the metalanguage.  Tarski
went into great detail about why the predicate istrue can only be used
at the metalevel, not at the object level.  If I ask the question,
"Is p true?", the proposition p may be stated in the object language,
but the question is stated at a metalevel that asks what would be
the denotation of p in a depiction that corresponds to the actual world.

> The mapping to databases is quite clear. Robots are very complicated, 
> and probably will have many representations of various kinds of information 
> serving many purposes. But these will all be representations of the 
> environment, and the interactions between them will involve the transfer 
> of information, so that questions of validity and correctness will be 
> important. So each internal representation will have to have some kind 
> of semantic account given of it, or internal comunication wil be meaningless. 
> It does not make sense to talk of translation between a description 
> and a TMT model of it.

I agree that practice in robotics is quite messy.  But I believe that
the notion of depiction is a useful basis for formalizing that mess
and talking about it in a precise way.  The relationship between a
KR language and a depiction is not one of translation, but an operation
that is formally identical to Tarski's model theory (the operations,
that is, not the metaphysics).  The relationship between a depiction
and the world is formally simpler (a one-to-one mapping of surrogates
to objects), but practically very messy because of all the complexities
of pattern recognition and mechanical arms.

> Current successes in robotic navigation hardly have any representation 
> of their world, either as description or as image. The ALFA architecture 
> of Rocky 3, for example, is designed to allow a heirarchy of increasingly 
> abstract accounts of the environment. Just how this is to be connected 
> to Krep is not yet worked out, but there would seem to be no need to 
> introduce this mysterious image-like (database-like?) entity between 
> one level and onother, and 'abstraction' is a relationship between
> descriptions, 
> not between a model and a description of it.

Yes.  The early robotic systems tried to simulate a human-like level
of thinking about the world.  The recent systems have been more
successful in modeling an insect-like level of perception and reaction.
But as you pointed out, the question of how that level is related to
a symbolic KR level "is not yet worked out".  I believe that is where
the depictions come in:  they are symbolic structures that can be
related to a KR language by well-understood methods, and they have
a mapping to the environment that can utilize the lower-level
perceptual and motor mechanisms of the robot.

> ... Commercial databases are not very closely connected to robot 
> worlds, and never will be. In any case, i think - though this is not 
> the place to have this argument - that most of our informal conceptual 
> apparatus - 'common sense' - is not closely related to perception 
> either: I think we have other ways of 'grounding' ourselves in reality, 
> including linguistic and social ways. For now, i merely observe that 
> robotics is largely irrelevant to the current discussion.

I was simply making the point that the models or depictions can help
to clarify computational practice in two widely divergent fields:
robotics and DB theory.  In the current work on Enterprise Integration,
these "not very closely connected" areas are coming together:  the
accounting DB, is related to the manufacturing DB, is related to the
engineering DB, which is related to the CAD/CAM system, which is
related to the automated manufacturing systems.  It is important to
have a theoretical framework that can formalize practice in all these
areas and enable language and metalanguage about them and their
interrelationships with one another and with the physical world.

> You can object as strongly as you like, but you have given me no 
> reason to withdraw my observation that the universe of a model can be a 
> set of anything whatever.

You can observe as strongly as you like, but you have given me no reason
to withdraw my suspicion that you have never considered the computational
mechanisms for relating your symbols to the physical objects of your models.

> Incidentally, I don't want to waste more time having these arguments about 
> philosphical scholarship, but Quine and Carnap both used what I have 
> been calling TMT. Montague, as you complained earlier accepted a realist
> account 
> of model theory. You can have Goodman and Barwise, although 'working' Situation 
> theory seems to extend rather than reject the model-theoretic 
> perspective: it also gives a recursive account of how language is attached 
> to (in this case, a part of) the world. It would be better if you stopped 
> citing philosophers all over the place. In return I will stop accusing 
> you of idiosyncracy, OK?

I just want to make one very clear distinction between Tarski's model
theory and the metaphysical question "What is an individual?"  I don't
believe that we have any quarrel whatever about the formal operations
of model theory.  Our disagreements have been over the separate issue,
which Tarski, Schoenfield, and other mathematical logicians have never
discussed, of whether the individuals in a model may or may not be
physical objects.

If we can agree upon the distinction between depictions and the world,
then we can dispense with all the metaphysical arguments and philosophical
questions about who said what.  Then we are left with computational
questions of how do we define KIF and CGs and how do we implement them
in an AI system.

> ... Why would you WANT to 'construct a model that 
> you can represent in a computer'?? What a strange thing to do! 

That is the kind of statement that drives me to historical and
scholarly citations.  How else can I counter that statement?  It ignores
common programming practice in a great many areas.  We have just been
talking about databases and robotics.  Do you want to get into another
debate about virtual reality?  About simulation systems?  All of these
areas and many more build and manipulate structures that look much
more like models than like languages. 

> ... I claim your
> four-part distinction is unclear and muddled....

Pat, I am trying as best I can to reach some kind of workable consensus.
You seem to agree with Jerry Aronson, with Len Schubert, and others.
I also have no difficulty in agreeing with Jerry and Len.  I am
quite willing to modify my diagram to get some form that we can all
agree on and that would provide sufficient computational machinery
to formalize current practice in AI, DB, robotics, virtual reality,
simulation studies, etc.  All of these areas are customers for the
work we are doing on KIF and CGs for the ANSI IRDS and Communications
committees and for the Knowledge Sharing Effort.  Jerry's term
"depiction", if formalized properly, seems to be a useful step
towards a consensus that would enable us to agree on the computational
matters while keeping our metaphysical beliefs to ourselves.