SUO: Re: Formal SUMO Draft -- *Date 04 Feb 2002
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JA = Jon Awbrey
RS = Randall Schulz
SUO WG Members,
I would like to take up Randall's comments in more detail.
JA: In my opinion it is a fundamental mistake to specify
a particular logical language, for example, KIF or
any other, as a part of the compliance conditions.
This would be as bad a practice as stipulating
that a compliant ontology has to be written in
English as opposed to French or German, or to
use an even more notorious analogy, that
a program has to be written in ADA.
JA: Requirements should be specified at a higher level
of abstraction and generality than any particular
ontology oriented logical formalism.
JA: Among the more deleterious side-effects of
thinking in only one language is a constant
tendency to confuse that language with reality.
RS: I do not agree.
RS: KIF neither imposes or implies any particular ontological
commitments nor does it dictate any particular logical or
inferential systems. It is lax about things like strict
separation of function and relation symbols and does not
itself demand a single arity for each function or relation.
It permits constructions that go beyond first-order logic.
But all those restrictions 'can' be imposed by its users
or by implementations.
Again, I continue to be shocked by statements like this.
It is the sort of thing that could only be said by folks
who have not yet strayed very far from the farms of their
childhood familiars. I have consistently, that is to say,
persistently, called your various levels of attention to
all sorts of significant, theoretically substantial, and
practically crucial variations in the concrete implements
of our logical projects, all them widely discussed in the
literature for tens, hundreds, if not thousands of years.
I have done this ever since someone first wrote out a list
of things that they just assumed were taken for granted by
all concerned and beyond all rational and serious question.
They are not beyond reasonable question, not by any means,
and most of them will make a critical difference to our
chances of effective, efficient, and practical success.
RS: I do not see what's to be gained (or, even, what is meant) by
specifying requirements "at a higher level of abstraction".
In fact, requirements specifications are scarcely more
tolerant of ambiguity and informal constructs than are
computer programs, ontologies, or proofs themselves.
"I do not see ..."
"I do not hear ..."
I see-hear these disclamors so often now --
I keep waiting for the other monkey to drop.
I meant exactly what was meant by all of our computer science profs
when they taught us to strive for abstractness and generality in our
programs, in a balanced trade-off with the other factors, to be sure.
Given the assignment of writing a program: "To compute the square of
a number", the person who interprets that indefinite article "a" as an
existential quantifier and then writes a program that returns the square
of his or her favorite number, well, that is a person who has yet to grasp
that the essence of a program is to do its duty for a whole class of inputs,
and not just for the select few that its maker, in his or her finite wisdom,
happens to favor.
We are trying to write the job description of a successful
candidate ontology. By "abstract generic specification"
in this context I only mean what common sense dictates,
that the requirements speak to the real qualifications
of the job in question. If you read an employment ad
that says something like: "Must be able to defeat the
current CEO, Mountain Man Mike, in a contest of his own
choosing, well, I think that anybody would smell a skunk,
and that is the scents against which I aimed my objection.
RS: The tendency to confuse descriptions with the described
("the map is not the terrain") is a property of human
cognition (of sloppy thinking, at that), and is not
principally a property or effect of the language
or the style of description.
What I said is this:
JA: Among the more deleterious side-effects of
thinking in only one language is a constant
tendency to confuse that language with reality.
I did not blame the instrument. I attributed the chronic aberration to
the observer who imagines that a monocular perspective is always enough.
The fixation in one language, one frame of reference, one coordinate
system, one basis of representation, leaves one susceptible to all
sorts of artifactual biases that become incorrigible for the lack
of an alternate control, a comparative check. And then one is
always saying stuff like "I can't see any bias in my view".
Saying stuff like that is one of the most telling of all
the symptoms of myomonocyclopia.
The facts are that any concrete syntax, as a concrete embodiment
of structure -- you might even say as a "physical symbol system",
will have characteristics of its own that are not all that well
related or conducive to conveying the features of any objects
in reality that you would use it to describe. These are the
artifacts of the instrument or the impedances of the medium
in question. There is no luminiferous ether here either.
But if it's the only medium that you have ever inhabited,
then you will find it nearly, all too nearly impossible
to reflect on the refractory properties of its conduits.
But once you get a sense of the objects themselves and
come to know their actual shapes, which you have to do,
for all practical purposes, by seeing them presented
in many different languages, media, and perspectives,
then you can sort out their proper properties from
the artifactual distortions of the grosser medium.
You may think that this is just a matter of cognitive psychology,
with regard to which the ideal of logic remains aloof and immune,
and you can try to dismiss it all as "sloppy thinking, at that",
but I have seen otherwise careful thinkers be led astray by the
wily deceptions of a monoclonal syntax.
Perhaps a few concrete examples would help me to explain what I mean
about confusing the features of a language with the features of the
objective reality that it serves to convey, tho' obscur'd, to us,
and at times, it seems, almost in spite of itself.
I was discussing this invariance issue
with Chris Menzel on the Ontology list,
some excerpts of which I will put here:
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Subj: Zeroth Order Theories (ZOT's)
Date: Sun, 27 Jan 2002 00:00:54 -0500
From: Jon Awbrey <jawbrey@oakland.edu>
To: Ontology <ontology@ieee.org>
CM = Chris Menzel
JA = Jon Awbrey
CM: Well, ignoring the inference from "S thinks baroque music is good"
to "S thinks anything baroque is good", as in music so in logic.
Detail and ornamentation are good when they have a purpose.
My objection to your stuff, as clever and even as elegant
as it might be, is that, as far as I can see, it just has
no purpose. It either provides nothing that isn't already
available in familiar (and generally far more straightforward)
forms, or else it does things that appear to be utterly pointless.
CM: What are the data structures depicted by your ASCII art *for*?
JA: They are for representing the same things that propositional expressions
in every other adequate syntax represent, only with a better articulation
of the invariant structures in these objects themselves and thus with what
most folks who consider the matter would consider a better conceptual grasp
of these objects, and, incidentally, but not entirely coincidentally, with
a better address of their computational complexity and thus with a better
mean-real-time computational performance, other things being equal.
CM: Sounds good, but I really have no idea what you mean by the invariant
structures of propositional expressions that would make this claim true.
Perhaps you could tell us. The only invariant structures I can think of
(e.g., some representation of indicative statements, some representation
of boolean operators, operator scope, etc) would, as far as I can see,
be pretty much as fully articulated in one representation as another.
Though "degree of articulation" itself is an awfully vague and
subjective notion to carry much scientific weight.
JA: When I speak of "propositions" at this level of glibness,
I am of course speaking with a forked tongue, and here
is just one of several explanations that I have given
of the quasi-commutative diagram that explains the
forking of it:
| If this is starting to sound a little bit familiar,
| it may be because the relationship between the two
| kinds of pictures of propositions, namely:
|
| 1. Propositions about things in general, here,
| about the times when certain facts are true,
| having the form of functions f : X -> B,
|
| 2. Propositions about binary codes, here, about
| the bit-vector labels on venn diagram cells,
| having the form of functions f' : B^k -> B,
|
| is an epically old story, one that I, myself,
| have related one or twice upon a time before,
| to wit, at least, at the following two cites:
|
| http://suo.ieee.org/email/msg01251.html
| http://suo.ieee.org/email/msg01293.html
|
| There, and now here, once more, and again, it may be observed
| that the relation is one whereby the proposition f : X -> B,
| the one about things and times and mores in general, factors
| into a coding function c : X -> B^k, followed by a derived
| proposition f' : B^k -> B that judges the resulting codes.
|
| f
| X o------>o B
| \ ^
| c = <x_1, ..., x_k> \ / f'
| v /
| o
| B^k
|
| You may remember that this was supposed to illustrate
| the "factoring" of a proposition f : X -> B = {0, 1}
| into the composition f'(c(x)), where c : X -> B^k is
| the "coding" of each x in X as an k-bit string in B^k,
| and where f' is the mapping of codes into a co-domain
| that we interpret as t-f-values, B = {0, 1} = {F, T}.
JA: In short, there is the standard equivocation ("systematic ambiguity"?)
as to whether we are talking about the "applied" and concretely typed
proposition f : X -> B or the "pure" and abstractly typed proposition
f' : B^k -> B. Or we can think of the latter object as an approximate
code icon of the former object.
JA: Anyway, these types of formal objects are the sorts of things that
I take to be the denotational objects of propositional expressions.
These objects, along with their invarious and insundry mathematical
properties, are the orders of things that I am talking about when
I refer to the "invariant structures in these objects themselves".
JA: "Invariant" means "invariant under a suitable set of transformations",
in this case the translations between various languages that preserve
the objects and the structures in question. In extremest generality,
this is what universal constructions in category theory are all about.
JA: In summation, the functions f : X -> B and f' : B* -> B
have invariant, formal, mathematical, objective properties
that any adequate language might eventually evolve to express,
only some languages express them more obscurely than others.
JA: To be perfectly honest, I continue to be surprised that anybody
in this group has trouble with this. There are perfectly apt and
familiar examples in the contrast between roman numerals and arabic
numerals, or the contrast between redundant syntaxes, like those that
use the pentalphabet {~, &, v, =>, <=>}, and trimmer syntaxes, like
those used in existential and conceptual graphs.
JA: Every time somebody says "Let's take {~, &, v, =>, <=>} as an
operational basis for logic" it's just like that old joke that
mathematicians tell on engineers where the ingenue in question
says "1 is a prime, 2 is a prime, 3 is a prime, 4 is a prime, ..."
CM: But let me put my cards on the table. The reason I have
been challenging your views rather stridently is because
of your earlier portentous rumblings -- wholly devoid of
argumentation -- about the devastating consequences of
using KIF and other standard logic-based KR languages
for ontology. All that you have provided us with is
a repackaging of first-order logic, basic set theory,
and a bit of recursion theory -- in a word (or two)
nothing new, save some novel and perhaps heuristically
or pedagogically useful new representations -- which, in
and of themselves, I encourage and applaud. But your dire
warnings against the use of KIF and its ilk for ontology are
utterly without foundation. Frankly, you should retract them.
JA: I have already refined my criticism so that it does not apply to
the spirit of FOL or KIF or whatever, but only to the letters of
specific syntactic proposals. There is a fact of the matter as
to whether a concrete language provides a clean or a cluttered
basis for representing the identified set of formal objects.
And it shows up in pragmatic realities like the efficiency
of real time concept formation, concept use, learnability,
reasoning power, and just plain good use of real time.
These are the dire consequences that I learned in my
very first tries at mathematically oriented theorem
automation, and the only factor that has obscured
them in mainstream work since then is the speed
with which folks can now do all of the same
old dumb things that they used to do on
their way to kludging out the answers.
JA: It seems to be darn near impossible to explain to the
centurion all of the neat stuff that he's missing by
sticking to his old roman numerals. He just keeps
on reckoning that what he can't count must be of
no account at all. There is way too much stuff
that these original syntaxes keep us from even
beginning to discuss, like differential logic,
just for starters.
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Well, I found myself copying almost all of that exchange --
because it illustrates in more detail what I have been
trying to say here about enscouncing any fixed syntax
for logic in our SUO conformity clauses -- but the
line that I want to highlight right now is where
Chris says this:
CM: The only invariant structures I can think of (e.g.,
some representation of indicative statements, some
representation of boolean operators, operator scope,
etc) would, as far as I can see, be pretty much as
fully articulated in one representation as another.
"... as far as I can see ..."
My replies are this:
1. Operator scope is a property of the linguistic basis,
and not necessarily of anything in reality. Of course,
there may be properties of invariant dimensionality that
can be demonstrated to apply to relations in reality, but
there is nothing very automatic about proving these things
to be so, when and if they do indeed hold, and none of it
comes for free just from looking at the superficialities
of a particular syntactic representation. This error is
called "reifying syntax". It's the sort of thing that
modern logicians used to heap loads of ridicule on
pre-modern logicians for indulging in.
2. It is just not the case that the objective properties
of boolean functions, for instance, are "pretty much
as fully articulated in one representation as another".
RS: As it stands, the SUO-KIF requirement is not much more than
a statement that the Ontology shall be written in prefix form
using a Lisp-like S-Expression syntax plus some minimal dictates
on the lexical patterns used to separate numbers from variables
from named entities and some commitments about how quantifiers
are notated. It's hard to see how this curtails, constrains or
distorts ontological thinking or options or how it would impair
the ability of participants to fulfill the substantive goals of
the SUO endeavor.
"It's hard to see ..."
RS: I'm inclined to think that if some commitments aren't made,
the likelihood of progress is lessened. Since the choice
of language in this context is mostly a matter of choice
of notational conventions Given the range of notational
variation displayed in the literature, I don't even see
it as one of the more important choices to be made.
That is not how progress was finally accomplished
in the other sciences, empirical and formal, that
ran into the very same sorts of problems long ago.
What they all had to learn, the hard way, in time,
was more or less what one of my long ago mentors
would always say: "Labels Are Fables" (LAF).
What it means is that a particular language,
pure or applied, is like a particular basis
for an algebra or a space. You just cannot
take the particularities of the coordinates
all that seriously, but you can only get at
the form of the subtly underlying object by
looking at it through so many diverse types
of spectacles that you can be slightly more
sure that you are not just seeing the specs
on your own glasses anymore.
RS: To sum up, Logic 'is' the language.
KIF is a notation, co-equal to many others.
KIF is adequate, well understood and common.
It's no mistake to choose it for SUO.
One eye is co-equal to many others.
Cast out the eye that extends you?
Jon Awbrey
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