[From: Bruce Nevin (Wed 92014 10:35:52)]
An article on fuzzy logic in _New Scientist_ for February 8, pp 36-9,
has intrigued me. It's been several years since I read about Zadeh's
work. The perspective of HPCT has helped me to understand it in a new
way.
People are using neural nets to define fuzzy sets. These set
definitions--which resemble your "subjective probabilities," Martin--are
then provided to implementations of fuzzy-logic inference engines. In
a simplified example, a wash load has degrees of membership in fuzzy
sets involved in two (out of 12) inference rules, as follows:
Wash Load * Cloth Quality ==> Washing time
========= ============= ============
0.52 "Average" 0.39 "Soft" 0.39 "Short"
0.28 "Heavy" 0.70 "Generally Soft" 0.28 "Average"
ยทยทยท
------------
"Center of Gravity" 4.9 minutes
A "defuzzification" procedure that computes the "center of gravity" as a
definite number is mentioned rather than described in the article.
It seems to me that HPCT maintains what might be called virtual fuzzy
sets in real time rather than by this batch-mode external production of
them in a neural net system. Putting it this way provides access to a
currently very hot button.
To point this up, the box on p. 38 of the article describes Takeshi
Yamakawa's fuzzy controller and its solution of the "inverted pendulum
control problem." A shaft is mounted on a vehicle by a pivot. The
vehicle has angle and velocity sensors for the shaft and velocity
sensors for the vehicle. The problem is to keep the shaft vertical by
moving the vehicle, much as one would balance a stick on the palm of
one's hand. The HPCT solution is obvious. The fuzzy controller cannot
be robust under disturbances such as tilting the table, turning on a
nearby fan, etc. But this is thought of as real hot stuff, gets
megabucks of support in Japan, and now elsewhere throughout the world.
The popularity of fuzzy logic stems probably from the craving to see
the whole world from the Principle level, in terms of programs, no?
Can we show how HPCT maintains the virtual equivalents of fuzzy sets and
does the equivalent of fuzzy inference for this sort of control?
Conversely, are fuzzy categories not needed on the program level?
Consider here Bill's (920225.2230) example "I've been rich, and I've
been poor, and believe me rich is better." Is this not just what you
were talking about, Bill? The equivalent of fuzzy sets and fuzzy logic
instead of discrete categories and binary either/or logic.
-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-
Chuck Tucker (920225) --
citations of studies that involve disturbances and disruptions within
interaction of two or more persons
Brad Goodman did some work here 8-10 years ago involving an instructor
and a learner separated by a screen, much as Bill has discussed. I have
looked for some old BBN reports describing this work but haven't found
it yet. I'll keep looking, but meanwhile here is a possible lead for
you to follow up.
-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-=+=-
Avery (2/14/92, 2/15/92) --
Your explanation to David about why you think the Diverian approach is
all post hoc rationalization" did not explain. Do diverians reject in
principle any attempt to predict "what sentences are grammatically
acceptable and what they mean" in a way that could be modelled on a
computer? Or do they reject rewrite rules manipulating phrase classes
(which I also do)? Or something in between?
Generative grammar of course does not provide any coherent account of
meanings, nor does LFG as a particular flavor of generative grammatical
theory. So the goal stated above must be reduced to predicting "what
sentences are grammatically acceptable" and leaving out differences of
acceptability on semantic grounds. Are you then saying that Diverians
reject the notion that grammatical acceptability is a central issue? In
that they would indeed be closer to Bill's position, as I see it.
Avery (27 February 1992) --
Looking at your example:
S
/ \
/ VP
/ / \
NP:SUBJ / \
NOM V NP:OBJ
N broke NOM
Jimmy N
the glass
Notice that you get an identical structure for
(1) Jimmy's betrayal broke up their marriage.
S
/ \
/ VP
/ / \
NP:SUBJ / \
NOM V NP:OBJ
N broke up NOM
Jimmy's N
betrayal their marriage
To distinguish these, you have another S subordinate to NP for (1), and
special metarules that say that rules like S ==> NP VP apply except when
the S is so subordinated, when other rules apply instead. Or in TG you
have rules operating on trees of phrase-class labels resulting from the
first sort of rules, producing deformed trees under these conditions.
In operator grammar, the reductions apply directly to words. All those
abstract names of phrase classes are unneeded and only get in the way of
connecting the words with the perceptions.
Corresponding to (1) we can also say:
(2) Jimmy's act of betraying someone broke up their marriage.
(3) Jimmy's betrayal broke up their state of being married to each other.
(4) An act broke up a state; the act was Jimmy's betrayal of someone;
the state was of their being married to each other.
These all exist. Regardless of the likelihood of one or another being
said, they all are English sentences conveying the same meanings
(quibbles possible about word choices, e.g. "state" vs. some other word,
but that's what Webster's advocates for "marriage" so I went with it.)
They are not related to each other in any obvious way in LFG or in GB
theory or in any other theory using a phrase-structure-based system of
rules. They are transparently related to each other in operator
grammar.
Furthermore, the transitions (by minimal sentence-differences) from less
explicit and less regular sentences to others that are more explicit and
more regular constitute the pathway by which one may arrive at a
semantic representation for sentences. After all the work of LFG, or
GB, or any of the other PSG-bound theories is done, a semantic
representation still must be devised, and a mechanism relating semantic
representations to words and syntactic structures on the one hand, and
to perceptions on the other. Typically, the semantic representation
includes features like [+abstract] to make the difference between
N=glass and N=marriage. This additional vocabulary and the additional
syntax governing its combinability has to be correlated with perceptions
(meanings) at the same time as the ordinary words do. In operator
grammar there are only words to be correlated with meanings. Those
words and the dependencies among them (whether obscured by reductions or made
explicit by undoing reductions, sometimes artificially) constitute the
semantic representation that is to be correlated with meanings.
This pellucid simplicity is forever beyond the reach of theories that
base themselves in PSG rewrite rules that manipulated the names of
classes of phrases. Saying that N-bar and N-double-bar are really just
instances of N, for purposes of determining the head of a construction,
is formalistic ad-hoc-ery. They are still different names of different
classes of phrases.
Conservation of resources on a small serial computer is not a germane
criterion if we are modelling human control of perception including
language.
Bill Powers (920224.0800) --
What's missing . . . is the sense of "Yeah, that's how I do it."
It appears that we keep the complexity of language control out of
awareness for good reason. There is just too much going on at once.
In order to describe it to ourselves and talk about it to one another we
must use that which we would talk about. But using it and making it
wiggle real slow under controlled conditions so we can get a good look
are mutually exclusive.
It could be claimed that the mental machinery
is invisible to the observer and that all we get out of it is the result.
But it seems strange to me that these methods use words, symbols, and rules
for manipulating them in the familiar way, except for the fact that they
propose content that is strange to me -- Bruce's expansions, and Avery's
NP, VP, trees, recursions, etc.
I argue that the "expansions" of operator grammar do not change the
content, only the form. The content is all familiar words, and the
pairwise word dependencies are all familiar. Some of the larger string
configurations are unconventional and unfamiliar. You get many
unconventional but possible sentences with other theories. With other
theories there is also new content, namely, a metalanguage vocabulary of
NP, VP, etc. and its syntax of trees, recursions, etc.
To the extent that the unconventional sentences are sayable and
understandable, however unlikely they may be in practice because of
their awkwardness and their violation of convention (which is why they
undergo reductions)--to the extent that they exist, they must be
accounted for by any theory. Operator grammar exploits them to provide
an explicit and informationally complete semantic representation for all
sentences.
I've tried for quite some time now (longer with Bruce) to elicit a
description of what a linguist is doing in the process of getting from a
received sentence to the structural analysis. What I get back is further
analysis -- i.e., you DO it, but you don't DESCRIBE WHAT YOU'RE DOING. I
don't want to know that "bite" is a word that takes two arguments, or that
"bite" is a PRED function of SUBJ,OBJ. That doesn't tell me what you're
doing in your head to get from sentences to those statements.
How a linguist gets from a received or imagined sentence to a structural
analysis is called linguistics and it may possibly be relevant to how a
language user gets from a received sentence to meanings. You say you
want a description of the former when in fact you want a description of
the latter.
I don't want
to know what a system or theory says about how the words are related --
what I'm trying to get is a description of what happens in your
consciousness when you begin with a new sentence (Josh felt Jean was
unsympathetic) and begin to re-represent it or something about it. Instead
of arguments developed from further application of the method in question,
I'm trying to hear the processes going on in present time in the person
offering those arguments.
You're asking for a freeze-frame account of category recognition,
mostly. I don't think I can break into the black box that takes sensory
input on one side and outputs a category on the other. I can introspect
on the sensory input, but I can only speculate on the process by which
it is categorized.
I look at the sentence (truncated from your last quoted above):
(5) I'm trying to hear the processes going on in present time.
I recognize I as a word that can't be an operator--it can't be said
"about" some other word. This is a zero-order word, in OG parlance.
I recognize 'm trying as a reduction of am trying.
Ignoring here what am..-ing is a reduction of, I recognize try as a word
that can be said "about" two other words. Two other words must be
present (said or zeroed in a reconstructable way). These are its
arguments. The first one has to be a zero-order word, preferably one to
which I am attributing human characteristics. The first one cannot be
an operator word. The second one cannot be a zero-order word, it has to
be an operator word.
I recognize that I is probably the first argument word that must be
present in order for try to be said. I recognize an operator-argument
dependency between try and I. (Please allow me to use meta-words like
operator and argument so as to talk about these things without imputing
to me the claim that I use these words internally in carrying out the
process I am describing.)
Furthermore, with try I have a strong preference that two zero-order
words be the same, namely, the first argument of try (which is I) and
the first argument of the operator word that is the second argument of
try. I haven't identified the second argument of try yet, but this
strong preference sets up some limitation as to what sort of word it
might be: it must be something that could have I as its first argument.
Also under try, there is a strong preference for reducing the repeated
first argument and the operator to the preposition to plus the operator.
I recognize the next word as the preposition to. Given the preceding, I
recognize this as a reduction of I as argument of a following operator
word. (This dependency could be made explicit by "expanding" to "I'm
trying that I should hear" but we need not do that expansion to get at
the dependency.)
I recognize hear as a word that cannot be said without two other words
present. The first argument must be a zero-order word. The second
argument must be an operator word. (When I say I hear John, I mean I
hear John doing something. The process of and justification for
reducing dually-classified words to a single class is a separate issue
that we can take up if it troubles you.)
Given the preceding, I recognize that the second (reduced) occurrence of
I is the first argument of hear.
I don't have time to continue this, but perhaps this gives the flavor.
Is this an accurate representation of what goes on in a language user in
real time? I couldn't prove that. But I think a model could be built
to do this in a convincing way. One's theory of language filters what
it is possible to perceive about one's control of perceptions resulting
in language. Having a least theory, that imports the least structural
baggage of its own, is I think of critical importance. Alternative
theories with which I am familiar are over-structured.
I've spent too long on this. Got to run.
Bruce
bn@bbn.com