Re: Responding to all those messages
Message-id: <>
Date: Sun, 9 May 1993 20:06:18 +0000
To: sowa <>,,
Subject: Re: Responding to all those messages

My mailer doesn't number messages like your MM, so I have to 
guess which messages you refer to. Some of them were probably 
not circulated to all of Interlingua, so if people are still 
following this debate, they will miss some of the backreferences. 
I have inserted brief notes to help clarify some of them, in 

These recent exchanges have certainly become clearer. I think 
we now both understand what we are talking about, and how we 
disagree. But it is still a real disagreement, both of content 
and style.

This is the last from me for a while on this debate, so let me 
say its been fun. Hope someone else has enjoyed it too. Thanks to
all who encouraged me to continue, and who refrained from telling 
me to shut up.

>> ... I could rephrase [Aronson's point] [[a philosopher 
quoted by John as making his points for him, but whose quotes 
seemed to me and Schubert to be compatible with our view]] as 
saying that the way in which a 
>> theory can describe the world must depend on what entities it - the theory - 
>> hypothesises to exist. 
>Fine.  This is a point on which we have no disagreement.

I'm tempted to slip back into debate mode by pointing out that if the 
theory hypothesises, say, trees, then trees are the things it 'hypothesises 
to exist', rather than a data structure of some sort. But that would just 
be just scoring points, so I won't do that.

>> ... Now, lets forget NL and think about these mental (or computer) 
>> representations. These, we agree(?), are what is meant by knowledge 
>> representations. 'Making these explicit' IS the processing of designing 
>> Krep formalisms and writing axioms[*1] in them, right? And these are the 
>> things whose relations to the world is described by semantic theories. 
>> That is exactly what I have been (intransigently) saying and you have 
>> apparently been vehemently denying. Or are you going now to say that 
>> there is yet another layer between these and the world? Where will this 
>> erection of mathematical barriers between beliefs and reality ever stop?
>I think I see one of the underlying causes of our disagreements.
>When I talk about things inside the computer (for simplicity, let's
>avoid both mental models and NL for the moment), I distinguish those
>things that are language-like from those that are model-like.  The
>great flexibility of programming languages like LISP and Prolog allows
>AI programmers to move very smoothly from language-like representations
>like KIF to model-like constructions that serve as internal surrogates
>for some physical systems.  Because those languages move so easily from
>one mode to the other, AI programmers don't always distinguish them.

Indeed, this is the source of a disagreement/misunderstanding. 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. (We can play the citing game back and forth to no 
purpose, so I'll just indicate that I know this is a popular perspective.)

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). 

By the way, this distinction between two kinds of Krep, one language-like 
and one which carries meaning by being similar to the world rather than 
describing it (see earlier messages), reminds me very strongly of the 
wellknown debate between mental descriptions and mental images. You have 
not used the term 'image', but these model-like things which are similar 
to the actual world seem to correspond quite closely to Sloman's old notion 
of a 'direct' (as opposed to a 'Fregean') representation, which began 
this controversy some 25 years ago. I have elsewhere argued at length 
against much of the discussion of the idea of image-like representations, 
and won't repeat all that here: suffice it to say that I think that this 
distinction, while meaningful, is often inappropriately applied to 
computer representations.

>The distinction is probably clearer in database systems.  I regard 
>SQL as an example of a language that is used to talk about a database,
>which I regard as a model.  A relational DB, for example, has a set
>of individuals (the data elements stored in its tables) and a set of
>relations over those individuals (the tables themselves).  SQL, for
>all its faults (which I have discussed with great disgust), has the
>expressive power of first-order logic.  The SQL language can be used
>in several ways:  
> 1. For defining the tables and their formats.
> 2. For populating them with individuals (i.e. DB updates).
> 3. For asking queries, which corresponds to the process of evaluating
>    the denotation of a formula in terms of the model.
>Please excuse me for being "pedantic" in explaining what you probably
>already know in great detail.  But I need to go into the details in
>order to show exactly what I mean when I say the AI languages are being
>used in two very distinct ways.  They are sometimes being used like
>SQL to make assertions and ask questions.  But at other times, they
>are being used to construct what I call "models", which are of the
>same nature as relational databases -- from an implementational point
>of view.  But from a logical point of view, those "models" serve the
>same purpose as Tarski's models when they are used to answer questions
>(i.e. they are the structures in terms of which the system computes
>the denotations of formulas).

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. 

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'). 

>From your constructivist perspective, in which models must be datastructures, 
this might not be true. This is one reason I find constructivism unattractive, 
but each to his own. My only purpose in keeping on about this is to resist your 
repeated implication (by assumption) that we must play things your way.

>> First, there is no reason why this should be computable! (I have referred 
>> to this mistake in an earlier message, but you did not reply to the point.) 
>> Model theory is not a theory of how a model of a formalism can be computed: 
>> it only undertakes to specify how the truth conditions depend on the syntax. 
>> When a 'model' is defined as a set D together with a set of relations,
>> nothing is said or implied about whether that set could be computed.
>Now I'm accusing you of long-windedly expostulating on the obvious.
>I thought that we had agreed many notes ago that we weren't disagreeing
>about any of Tarski's formal operations, nor about Cantor's formal
>constructions.  When I used the phrase "formal and computable", I wasn't
>suggesting that the two words were synonyms -- if I believed that, I 
>would have used only one.  To repeat:  formal is a prerequisite for
>computable, and computable is a prerequite for being implementable
>on a digital computer.  But there are formal things that are not
>computable, and things that are computable in Turing's sense that
>couldn't be implemented even on a computer that incorporated every
>atom of the universe.

This completely misses the point. I did not accuse you of confusing 'formal' 
with 'computable'. However, "formal and computable" entails "computable", 
which is what I was referrring to: and you have not responded to my point here. 
However, rather than go on and on about this, I think I now understand why you 
believe models are computable. Just stop insisting that they must be.

>> Second, to say that the idealization must be a mathematical construction
>> not mean that it is a construction made out of 'mathematics', where that is 
>> some strange abstract kind of stuff.
>No.  That's why I like to use the term "data structure".  It is a term
>that everyone tuned in to these mailing lists understands, and it is
>clearly distinct from the physical objects in the world outside the computer.

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.)

>> And notice that I have, here, referred to the actual gas molecules. Len's 
>> idealisation doesn't refer to them, but it is evidently possible to do so;
>> 1why shouldn't another, less idealised, theory - for example, a theory about
>> degree of idealisation of the first theory -  do so?
>At the time that Boltzmann was formulating his "model", the atomic
>hypothesis was widely accepted only in chemistry.  Ernst Mach fought
>against it up to the end of the nineteenth century.  It wasn't until
>Einstein's famous paper on Brownian motion that the last vestiges of
>resistance to atoms disappeared.  Boltzmann committed suicide in
>1906, partly because of depression caused by the widespread rejection
>of his hypothesis.

Fascinating, but not relevant to the example or the point it was making. 
[[Which was concerned with 'idealisations', eg of a gas a lot of small 
spherical objects; Schubert's example. Sowa wanted 'idealisations' to be 
his intervening datastructures. I responded that it was better to regard 
them as a way of fitting a theory onto the world, so that the billiard-balls 
could be small spheres of space surrounding actual gas molecules.]]

>My point is that a physical theory, like an engineering drawing,
>starts out as a mathematical construction whose terms cannot with
>any certainty be related to real world "things".  If the theory is
>successful, we may come to believe in the existence of those "things",
>but we have to be able to construct models from sets, data structures,
>or other abstract stuff in both physics and engineering.

There is a deep metaphysical disagreement lurking here, quite separate 
>From your 'database' reasoning of why models should be datastructures. 
I've referred to it in earlier messages, but will try to state it more 
clearly below.

>I consider a theory to be the deductive closure of a set of axioms.

OK, me too (although I am sometimes loose, in these discussions, about 
'deductive closure', I confess, and have used 'theory' to refer simply 
to a set of axioms.)

>I consider an axiom to be a proposition assumed as a hypothesis for
>the purpose of exploring the implications of a theory.  The distinction
>between "sentence" and "proposition" is another topic that could get us
>into an endless round of notes. 

I agree, and agree with your definitions and discussion here, which is all 
perfectly conventional.
>> Sowa:
>> Krep <==> Model <--> World
>No.  As I pointed out above, the languages used in AI are sometimes
>used for language-like and sometimes for model-like purposes. 

As Len Schubert said, this is just a vocubulary clash between us. In 
talking about Krep, I mean to refer to anything in the computer that 
represents knowledge of the world. 

 I would
>say that KIF and CGs are both pure language-like kn. representations.
>They can be used to talk about the world, but their mapping to the
>world in a computer implementation is by means of a model-like scene
>representation that would be used by a robot-driver:
>   Krep (e.g. KIF or CGs) <--> Model <--> World

No, it 'IS' not that way. (Is! Isn't! Is!! Isnt!!) That might be one way 
to do it, but I think its a wrongheaded and confusing way to do it, and it 
is not in any way required by the use of model theory. 

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.

>If you want to bring NL into the picture, it would be placed on the left:
>  NL <--> Krep (e.g. KIF or CGs) <--> Model <--> World

Ogden & Richards, like many philosophers, take 'language' to mean NL, and 
we have to bear this in mind when citing them. So lets not cite them when 
discussing Krep, and agree to leave NL out of the discussion.
>...... I would say that some
>human thinking is fairly well modelled by inference, but much of human
>thinking is better modelled by mental manipulation of image-like or
>model-like representations. 

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.

>> I expect you will agree with all this, but still insist that models be 
>> built only from unreal objects, perhaps referring us your four-way split 
>> again to justify this.
>My four-way split is motivated primarily by my work with databases,
>rather than my work with NL.  In DB theory, it is common to make a
>very clear distinction between lexical object types (LOTs) and
>non-lexical object types (NOLOTs).  They say explicitly that NOLOTs
>like people and trees cannot be flattened out and stored on a disk;
>instead, they must be represented in a database by "surrogates",
>such as "tuple identifiers".  Those surrogates are very closely
>related to the GENSYMs used in LISP to represent the external NOLOTs.
>My claim is that the DB people have been making a distinction that
>has proved to be very useful to them, and I believe would also be
>very useful to AI. 

That helps me understand your thinking. (I wish you had referred to 
databases earlier!) 

Of course this distinction is useful. This talk of LOTs 
and NOLOTs is simply the distinction between names (notice 'lexical') and 
things, or symbols and their referents. So AI already has this 
distinction (and model theory is the usual account of it.) That fits 
perfectly with the account I prefer of databases. 

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
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 would agree that those AI researchers who have
>never attached their systems to a robot manipulator have a tendency
>to ignore or downplay the importance of separately thinking about
>representing the language and representing the models.But I will
>further claim that those AI people who are working with robots make
>a distinction between models in the machine, the real world situation,
>and the kn. rep. languages.  I believe that if the Knowledge Sharing
>Effort is going to link up with systems dealing with manufacturing,
>database systems, and other commercial programming problems, it will
>become increasingly important for them to make that distinction as well.

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[*1], 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.

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
not between a model and a description of it.

Anyway, many, probably most, representational issues are concerned with 
representing information which is not related to any robot's 
sensors. 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, 
inclusing linguistic and social ways. For now, i merely observe that 
robotics is largely irrelevant to the current discussion.

>I strongly object to your identifying (notice that I avoid the loaded
>word "confusing") that body of work in mathematical logic with what
>you call TMT, which permits the individuals to be identifed with
>NOLOTs without specifying the operational mechanisms by which that
>identification is to be carried out.  Those philosophers who did want
>to address that mapping between symbols and the world (e.g. Carnap,
>Goodman, Quine, Montague, Barwise, and others) have all developed
>highly "idiosyncratic" theories, to use your term. 

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.

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
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?

The only people
>who have used model theory without such an accompanying philosophy
>are those who have been addressing the technical issues of the
>formalism -- that includes most textbook writers, including our
>friends Nilsson and Genesereth -- but did not want to get bogged
>down in the numerous philosophical issues.

As I have said earlier, there is no need to get so bogged down. Your 
metaphysical scruples may make you uncomfortable in referring to sets of 
real things without first specifying exactly how they are to be perceived 
and identified, but there is no reason why anyone else should be so 
concerned (unless they follow your particular beliefs).

>I do believe that a clear distinction between the models of model theory
>and the real world helps to clarify many philosophical issues.  But as I
>pointed out above, such mundane matters as relational databases and robot
>manipulators drive us to exactly the same distinctions.

I draw different conclusions from the mundane examples. Whatever you call 
a 'model' seems to me to be a representation, and questions of its meaning
 - in the world - and intertranslatability with other representations are 
best approached by asking for a precise account of how it (they) might 
describe things. So these 'models' - if database-like - are sets of ground 
assertions, and their properties are being studied by Reiter and others; 
if robot-blackboard-like, then they probably consist of collections of 
various representations, mostly descriptive; and if image-like, then we 
have to get involved in a different debate.

>.....  But I'd like to make the efficiently
>computable stuff the path of least resistance.

Thats kind of a tautology. But more seriously, there's a debating ploy 
being used here: you have somehow associated your position with efficient 
computability, obviously a Good Thing. I have seen not the slightest 
argument anywhere in this discussion (or anywhere else) that suggests 
why anything should be more efficiently computable if we refuse to 
believe that symbols denote objects.

>> ... The ambiguity of interpretation emerges as
>> the fact of there being a large number of ways of interpreting the theory
>> over the domain of real colors, but does not mean that defining any such
>> interpretation involves real-color theory.
>I think this passage touches on our misunderstanding.  In fact, this
>is one reason why I want to make the distinction between models and
>reality.  If you give me a theory of colors (a collection of predicates
>for colors and some axioms that relate them), I can construct a model
>that I can represent on a computer without using any crayons from the
>big Crayola box.  The model in the computer is made up of data structures
>that I can query with the SQL language or with KIF or CGs. 

Yes, it does illustrate it. Why would you WANT to 'construct a model that 
you can represent in a computer'?? What a strange thing to do! Surely what 
you want to do is use your representation to draw conclusions about 
something. {Care needed, I know, because in a sense, performing an inference 
IS trying to construct a model, and so such a model, if constructed, might 
be a counterexample to a proposed goal. I don't think yo umean this, however, 
because these counterexamples are neither image nor database)

But when I
>want to relate that model to the real world, then I have to bring out
>my Crayola box or find a physicist who specializes in optics and has some
>instruments that can be hooked up to my computer representation.
>But when I use KIF, CGs, or SQL, I agree with you that I am talking
>"about" colors.  But the link between those languages and my Crayola
>box or the physicist's instruments is only indirect through the data
>structures in my computer.  When I say "Green is between yellow and
>blue on the spectrum", I am talking about colors, not about data
>structures, Crayola boxes, or optical instruments.  But when the
>truth of that statement is evaluated in my computer, it is
>done either syntactically by proving a theorem or semantically by
>checking the position of green, blue, and yellow in my data structures.

Nice example. Surely if it needed to be checked semantically, the 
robot would need to go look at the Crayola box itself. If it already 
has an internal representation of the color wheel, so it can check 
whether "Green is between yellow and >blue on the spectrum" with its 
eyes shut, then that 'model' has a much stronger semantic status 
than just being a TMT model. If that is all it were, there might be 
lots of other interpretations as well, and the conclusion would not 
be at all firm. I can't correctly infer P from P's being true in just 
one TMT model. No: this internal spectrum representation has the 
semantic status (and computational role) of a whole lot of ASSERTIONS 
ABOUT the relative positions of Crayola colors. It is a database of color 
information, maybe: but thats not a model of assertions about color, 
but a LOT of assertions about color.

>I'm happy to say that my language is about the world, and I'm happy to
>let you do the same.  But I claim that my four-part distinction helps
>me to formulate a theory of how language relates to (or "is about") the
>world.  And I claim that such a distinction is useful for both
>philosophical and computational reasons.

Claim away, and good luck. I am all in favor of everyone claiming all 
kinds of things. But don't tell me (and others) that we are not 
allowed to say things that don't agree with your claims. I claim your 
four-part distinction is unclear and muddled, that you identify ideas 
that should be separated (for example: database, image and blackboard), 
that you misuse semantic ideas such as translation and inference,
and that your ideas serve only to introduce confusion into what was 
becoming a reasonably clear area of discussion. But that's OK: we dont 
have to agree on everything. 


I have your position clear now. You are indeed essentially a constructivist. 
You have also observed that we cannot talk (or think) about the world 
without using some kind of conceptual apparatus. You draw the conclusion 
that to talk of reality - especially when discussing meaning, perhaps - 
is somehow inappropriate, or at any rate deeply suspicious, because it 
seems to claim an impossible privilege; or at any rate, in order to talk 
of reality we have to be very careful to establish the edges of our 
conceptual language and exactly how it fits to reality: we have to have 
all issues of metaphysics and epistemology clear. You are impressed by 
model theory and want to use it, but must forbid talk of reality. Images 
provide a nice way to have the cake and eat it, since you can push all 
those nasty problems out of the semantic world into some other area which 
is bound to be a mess anyway. The database world has novel terminolgy 
for a familiar idea (as it has for all others) so you claim that this is 
actually a novel idea, and by identifying images with databases you make 
it all fit together.

Of course any account of the world must be through a conceptual framework, 
and sometimes a framework will not 'fit' some aspect of the world, so the 
relevant descriptions are impossible, and to access that part of reality 
we must make a change. But none of this means that any particular framework 
is in error: so in giving a semantics, we can use the one that happens to 
be convenient, just as we do in any other human enterprise. Of course then 
our semantics will be relative to, and depend for its security on, that of 
the framework we used. How could it be otherwise? Your worries about redwood 
forests and accuracy of measurements are simply inappropriate. They can be 
ignored for now. 

If we have ever have to create a theory of redwoods, then maybe we will need 
to be concerned with them. But look at the consequences of your insistence 
that models can't be real. If I ever try to make a CYCobotanist, according 
to you, I have a double problem of world modelling. I have to write axioms 
about trees and trunks and roots: but I ALSO have to write a Principia 
Foresteria, a set-theoretic account of what a reasonable model of the botanical 
theory will be like: but all made of sets (or data structures: a computational 
Principia). Why should I accept this double burden? It is completely
quite artificial, provides no new semantic clarity or computational
insight, and 
is only made necessary by your having some philosophical conversion on the 
road to Damascus. 

I don't accept it. I will go on talking about models of Krep formalisms made 
up of real, physical parts of the world, and I will mean what I say.

Pat Hayes

[*1] Some representations might be about internal things, of course, and some 
might be about other representations, so this is an oversimplification. 

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