Re: Communmicative PCT (was Quantum
Thoughts)
[From Bill Powers (2005.05.18.0444
MDT)]
Martin Taylor 2005.05.16.23.13 –
Have you considered the problem I’m talking
about?
Yes, we originally (mid 1980’s) were thinking in terms of sequential
dialogue acts, and the activity in the GPG chart moving from one point
to another, but quite early on we recognized the issues you raise.
The problem is how to express it on paper. It’s not easy, even in
verbose text, and it’s less easy in a static diagram. The best we came
up with is to supplement the diagram with text saying that many arcs
and nodes may be simultaneously active, and that even when there is
only one transition occurring, it occurs progressively, not as an
event in which the activity switches instantaneously from one node to
the next.
This is the problem with trying to
diagram the behavior rather than the system that is behaving. The
actual behavior will depend dynamically on how the interaction
goes…
What keeps a dialog organized is the intention of each party involved
and the effort to keep errors small.
Yes, that’s the underlying mechanism. But I think you are too
quick to dismiss the possibility of describing the likely behavioural
paths (note: “likely” not “possible”) in a
collaborative interaction. If the interaction isn’t collaborative, but
includes conflicting goals, then the problem becomes much less
well-defined. In a collaborative dialogue, the GPG seems to provide a
pretty reasonable cartoon description of the overt behaviour that
actually happens.
In the development of LPT (before its PCT-substrate was
recognized), the GPG developed from two sides: an intuition about what
one might do under different conditions of the state of communicating
the current message (at one level), and informal analysis of real
dialogues to see whether they took any turns that were not already
incorporated in the GPG. In retrospect, the intuitive analysis always
depended on the formula: “If I were in this situation, and wanted
that situation, what would I do.” In other words, asking about
the likely kinds of error that might be leading to dialogue output
to control a current perception. The observational approach was, of
course, subject to the qualification that, as third parties, we could
never be assured of our interpretations. The two together seem to
provide a consisten formulation, though.
In formalizing the grammar, the diagrammed GPG was ignored.
Instead, we started with an invented formal notation based on three
statements of fact (“real world” conditions unknowable to
the participants). The three statements were:
P1: The recipient has made an interpretation of the primal
message
P2: Whenever P1 is true, then the recipient’s interpretation will
be adequate
P3: It is not worth continuing to try to reach the state (P1 &
P2).
(quoted from Taylor and Waugh, “Layered Protocol Analysis of
Dialogue” in “Abduction, Belief and Context in Dialogue:
Studies in Computational Pragmatics, H. Bunt and W. Black, Eds,
Amsterdam, John Benjamin, 2000”). (Note: the “primal
message” is the originator’s reference for the state the
recipient should be in after the message has been correctly
interpreted)
Each participant (and any onlooker) may perceive any or all
of these propositions to be true, false, or indeterminate to some
degree. In other words, belief in their truth is a continuous (fuzzy,
if you like) variable.
If, for example, in a collaborative dialogue the originator
strongly believes P1 to be false, it will not matter to the originator
what interpretation the recipient believes she has made, but what the
originator does about it will depend on whether the originator
believes the recipient to believe P1 to be true – as well as whether
the recipient believes P2 if the originator believes the recipient
believes P1.
In a collaborative dialogue, both parties have reference levels
that all three propositions be simultaneously true. In a
non-collaborative dialogue, the reference levels for the two parties
may differ in respect of any or all of the three propositions. The
reason it is plausible to use a process model to regenerate the GPG
for a collaborative dialogue is that the reference values for all
propositions are assumed to be known, as are the possible mechanisms
available for output.
To explain this last, a mechanism for the example condition above
is to send a (lower-level) message that informs the recipient that the
originator does not believe the recipient to have made an
interpretation. The means by which that lower-level supporting message
is implemented is a question for the GPG at that lower level, just as
in the normal PCT hierarchy, the mechanism is unspecified whereby an
output of a higher-level control system affects its perceptual
variable.
Continuing with the formalization…
We recognize three variables connected with each proposition, all
of which take on a continuum of values that you might say range from
-1 to +1, or from minus to plus infinity. Let’s use -1 to +1 for
convenience. The variable correspond to the three main variables of an
elementary control unit (ECU): the perceptual signal, the reference
signal and the output gain.
Variable 1 is the degree of belief in the proposition (a
perception). Variable 2 is a goal for the belief in the perception (a
reference, which in a collaborative dialogue is +1). Variable 3 is the
intention to produce a change in the perception (the output gain). We
simplified the analyses by assuming the output gain to be constant, so
neither it nor the reference signals actually appear very much in the
formalism.
The notation we used was not very transparent, but it was the
best we could come up with. If participant A has a degree of belief x
about proposition P, we wrote x = A(b,P). For a goal, we substitute
“g” for “b”, and for an intention, we used
“i” for “b”. Since neither “i” nor
“g” are much used except for exposition, we usually elided
the “b” and wrote x = A(P).
The example above would be written “0 > Originator(P1)”
– zero is greater than the degree of belief the originator has that
the recipient has made an interpretation. If the Originator believes
also that the recipient believes that the recipient has made an
interpretation, we get
0 > Originator(P1) & 0 <
Originator(Recipient(P1))
The second term represents another perception that must be
controlled for the dialogue to progress in a collaborative way.
Indeed, as I mentioned in my previous message, we found that one (and
only one) more recursion is needed. the Originator needs to control
(b,O(b,R(b,O(P))) using O and R for Originator and Recipient of the
primal message. The revipient has a corresponding set of belief values
to control.
Given that there are three fundamental propositions and three
recursion levels (including the zeroth level of belief about the
proposition), each participant is controlling nine perceptions. The
values of these nine perceptions defines a point in a 9-D space, and
different regions of the space map onto the nodes of the GPG – at
least those that are likely to be occupied in a collaborative dialogue
do. They determine also the implementations of the arcs that connect
the nodes. If I remember correctly, when we itemized the
implementations of th arcs (including “do nothing because
perception matches reference”) we counted someting like 47
different plausible things that might happen at one dialogue level in
communicating one primal message.
Some, of course, are more likely than others. At the word level,
between people who talk the same dialect of the same language, and are
talking in a quiet environment, the primal message (the word) is
almost always going to be correctly interpreted (fact), and the
participants are likely to beieve that to be so. So, at O1, where the
word is delivered, the originator immediately believes P1, P2, and P3,
and that the recipient believes the three propositions, and that the
recipient believes the originator believes them. Knowing (or
believing) all that, the originator can, legitimately and
collaboratively, proceed immediately to the next word. Seldom will the
Recipient interrupt with a feedback message asking for clarification
at that (the word) level. So at that level, almost all of the 47
possibilities are essentially unused.
However, if the originator intends to explain General Relativity
to a precocious ten-year-old, the sequence of feedback messages may
last several years before the teacher and student both believe P1, P2,
and P3 and the two levels of recursion about each other’s belief
states. All 47 paths in the GPG (other than the “Abort”
paths) are likely to be well used over those year of passing that one
message.
It would be a real tour de force if you
could come up with a communication control system – even at just one
level – that would actually generate communications toward the end of
achieving and maintaining certain goal-states in the conversation, or
nonverbal states.
As you see, we’ve gone at least some way toward specifying such a
model through the formalism. Somewhere or other, I’ve diagrammed at
least a part of it in the visual language of control systems, but I
don’t remember where that was. If I run across the diagram, I’ll post
it. We have never tried to embody the formalism in working code, which
would be a major project, as it would involve not only the control of
nine perceptual variables at each level (no big deal), but also the
implementation of the perceptual input functions (read “language
understanding functions”) and the output functions (read
“language generation systems”).
A generative model, that is, as opposed
to a descriptive model – a system design such that two of them would
actually generate a dialog which you could then chart as a flow
diagram. It might be necessary to develop a limited vocabulary of
words designating nonverbal things that the parties are trying to
control by using the words on each other.
A toy of this kind might be do-able since it would eliminate the
need for the language systems, but it would still be, as you say, a
huge effort. It’s a little like what Allan Randall and I tried to do
years ago by building a “Syntactic Little Baby” (based on
your “Little Baby”) that was supposed to learn to perceive
and control a simple syntax that created a stream of As and Bs. Even
that turned out to be a bigger project than we had money for.
I know I’m describing a huge and
long-term effort. I don’t really expect you to abandon what you’re
doing to carry it out.
I’m glad of that 
But I hope the above helps people to understand a little of where
LPT fits on top of PCT.
Martin