Theme One Program • Motivation 6

Comments I made in reply to a correspondent’s questions about delimiters and tokenizing in the Learner module may be worth sharing here.

In one of the projects I submitted toward a Master’s in psychology I used the Theme One program to analyze samples of data from my advisor’s funded research study on family dynamics.  In one phase of the study observers viewed video-taped sessions of family members (parent and child) interacting in various modes (“play” or “work”) and coded qualitative features of each moment’s activity over a period of time.

The following page describes the application in more detail and reflects on its implications for the conduct of scientific inquiry in general.

In this application a “phrase” or “string” is a fixed-length sequence of qualitative features and a “clause” or “strand” is a sequence of such phrases delimited by what the observer judges to be a significant pause in the action.

In the qualitative research phases of the study one is simply attempting to discern any significant or recurring patterns in the data one possibly can.

In this case the observers are tokenizing the observations according to a codebook that has passed enough intercoder reliability studies to afford them all a measure of confidence it captures meaningful aspects of whatever reality is passing before their eyes and ears.

Resources

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Theme One Program • Motivation 5

Since I’m working from decades-old memories of first inklings I thought I might peruse the web for current information about Zipf’s Law.  I see there is now something called the Zipf–Mandelbrot (and sometimes –Pareto) Law and that was interesting because my wife Susan Awbrey made use of Mandelbrot’s ideas about self-similarity in her dissertation and communicated with him about it.  So there’s more to read up on …

Just off-hand, though, I think my Learner is dealing with a different problem.  It has more to do with the savings in effort a learner gets by anticipating future experiences based on its record of past experiences than the savings it gets by minimizing bits of storage as far as mechanically possible.  There is still a type of compression involved but it’s more like Korzybski’s “time-binding” than space-savings proper.  Speaking of old memories …

The other difference I see is that Zipf’s Law applies to an established and preferably large corpus of linguistic material, while my Learner has to start from scratch, accumulating experience over time, making the best of whatever data it has at the outset and every moment thereafter.

Resources

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Theme One Program • Motivation 4

From Zipf’s Law and the category of “things that vary inversely with frequency” I got my first brush with the idea that keeping track of usage frequencies is part and parcel of building efficient codes.

In its first application the environment the Learner has to learn is the usage behavior of its user, as given by finite sequences of characters from a finite alphabet, which sequences of characters might as well be called “words”, together with finite sequences of those words which might as well be called “phrases” or “sentences”.  In other words, Job One for the Learner is the job of constructing a “user model”.

In that frame of mind we are not seeking anything so grand as a Universal Induction Algorithm but simply looking for any approach to give us a leg up, complexity wise, in Interactive Real Time.

Resources

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Theme One Program • Motivation 3

Sometime around 1970 John B. Eulenberg came from Stanford to direct Michigan State’s Artificial Language Lab, where I would come to spend many interesting hours hanging out all through the 70s and 80s.  Along with its research program the lab did a lot of work on augmentative communication technology for limited mobility users and the observations I made there prompted the first inklings of my Learner program.

Early in that period I visited John’s course in mathematical linguistics, which featured Laws of Form among its readings, along with the more standard fare of Wall, Chomsky, Jackendoff, and the Unified Science volume by Charles Morris which credited Peirce with pioneering the pragmatic theory of signs.  I learned about Zipf’s Law relating the lengths of codes to their usage frequencies and I named the earliest avatar of my Learner program XyPh, partly after Zipf and playing on the xylem and phloem of its tree data structures.

Resources

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Theme One Program • Motivation 2

A side-effect of working on the Theme One program over the course of a decade was the measure of insight it gave me into the reasons why empiricists and rationalists have so much trouble understanding each other, even when those two styles of thinking inhabit the very same soul.

The way it came about was this.  The code from which the program is currently assembled initially came from two distinct programs, ones I developed in alternate years, at first only during the summers.

In the Learner program I sought to implement a Humean empiricist style of learning algorithm for the adaptive uptake of coded sequences of occurrences in the environment, say, as codified in a formal language.  I knew all the theorems from formal language theory telling how limited any such strategy must ultimately be in terms of its generative capacity, but I wanted to explore the boundaries of that capacity in concrete computational terms.

In the Modeler program I aimed to implement a variant of Peirce’s graphical syntax for propositional logic, making use of graph-theoretic extensions I had developed over the previous decade.

As I mentioned, work on those two projects proceeded in a parallel series of fits and starts through interwoven summers for a number of years, until one day it dawned on me how the Learner, one of whose aliases was Index, could be put to work helping with sundry substitution tasks the Modeler needed to carry out.

So I began integrating the functions of the Learner and the Modeler, at first still working on the two component modules in an alternating manner, but devoting a portion of effort to amalgamating their principal data structures, bringing them into convergence with each other, and unifying them over a common basis.

Another round of seasons and many changes of mind and programming style, I arrived at a unified graph-theoretic data structure, strung like a wire through the far‑flung pearls of my programmed wit.  But the pearls I polished in alternate years maintained their shine along axes of polarization whose grains remained skew in regard to each other.  To put it more plainly, the strategies I imagined were the smartest tricks to pull from the standpoint of optimizing the program’s performance on the Learning task I found the next year were the dumbest moves to pull from the standpoint of its performance on the Reasoning task.  I gradually came to appreciate that trade-off as a discovery.

Resources

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Theme One Program • Motivation 1

The main idea behind the Theme One program is the efficient use of graph-theoretic data structures for the tasks of “learning” and “reasoning”.

I am thinking of learning in the sense of learning about an environment, in essence, gaining information about the nature of an environment and being able to apply the information acquired to a specific purpose.

Under the heading of reasoning I am simply lumping together all the ordinary sorts of practical activities which would probably occur to most people under that name.

There is a natural relation between the tasks.  Learning the character of an environment leads to the recognition of laws which govern the environment and making full use of that recognition requires the ability to reason logically about those laws in abstract terms.

Resources

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Higher Order Sign Relations • 6

Re: Higher Order Sign Relations • 4
Re: Relations, Types, Functions
Re: CyberneticsCliff Joslyn

Cliff Joslyn recommends the following books.

Dear Cliff,

The following Survey page gives a hint of the tack I’ve been taking with category theory since the early days but definitely moving into higher gear during my year at Illinois in the mid 1980s.  John Gray taught a course joint between math and computer science on the Applications of Lambda Calculus and David Plaisted taught a course on Resolution-Unification Theorem Proving, both of which I took and followed up with independent studies.  I spent a heady year making the circuit between math, computer science, and psychology departments and a lot of what I work on today goes back to issues raised in those days.

I know that Survey from a couple years ago still looks a little sketchy but I’ll be working to make it less so as time goes by, especially if I ever get around to unpacking my notes from the basement boxes.

I have been sampling current approaches to categories at sundry sites around the web over the last two decades — John Baez, nCafe, nLab, Zulip Category Chat, Topos Institute, etc.  As great as all that is there’s a reason why it bears but tangentially on the questions I’ve been pursuing.  That has to do with the Peirce Factor and how far a given line of inquiry takes account of it.

As luck would have it, one of the texts John Gray used for his course, Lambek and Scott’s Introduction to Higher Order Categorical Logic, resonated strongly with themes I knew from Peirce and that led me to many adventures of ideas still in progress.  The following set of excerpts I shared with the Standard Upper Ontology Group back in the day may suggest the character of that work.

  • Lambek, J. and Scott, P.J. (1986), Introduction to Higher Order Categorical Logic

There’s a lot more to say, but that’s all I have time for today …

Regards,

Jon

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Survey of Inquiry Driven Systems • 4

This is a Survey of blog and wiki resources on Inquiry Driven Systems, material I plan to refine toward a more compact and systematic treatment of the subject.

An inquiry driven system is a system having among its state variables some representing its state of information with respect to various topics of interest, for example, its own state and the states of any potential object systems.  Thus it has a component of state tracing a trajectory though an information state space.

Elements

Background

Blog Dialogs

Developments

Applications

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Inquiry Into Inquiry • Discussion 5

Re: Inquiry Into Inquiry • In Medias Res
Re: Inquiry Into Inquiry • Flashback
Re: Inquiry Into Inquiry • Discussion 4

A quick review of the highlights so far, and then I’ll continue from the standpoint I indicated last time.  As you recall, Dan Everett opened with the following problem.

DE:
I am trying to represent two readings of the three juxtaposed sentences in English.  The first reading is that the judge and the jury both know that Malcolm is guilty.  The second is that the judge knows that the jury thinks that Malcolm is guilty.

Daniel Everett • Judge, Jury, Malcolm, Guilty • Graph 1

Daniel Everett • Judge, Jury, Malcolm, Guilty • Graph 2

Do these purported EGs of mine seem correct to you?

Dan’s initial question about logical graphs sent me further down memory lane than I usually go, to my first encounters with extensions vs. intensions in logic, intentional contexts, propositional attitudes, referential opacity, truth-functionality, and triadicity, puzzles about which my first logic prof sent me off to read Quine’s Ways of Paradox and a host of others.

I had been studying Peirce on my own through all my undergrad years and was fortunate at long last to find an advisor who was a fund of knowledge about Peirce and Pragmatism, not to mention the Ancients and philosophy in general.  In several of our discussions from those days I can remember expressing my hunch the problems of intentionality were not due to a distinct modality or quality of propositions but a different quantity or dimension of relations.  I did not get to Russell’s monographs of 1918 and 1913 until much later but when I did I was struck immediately by his use of graphs to represent relations, so like Peirce’s graphs for the logic of relatives.

Othello Believes Desdemona Loves Cassio

To be continued …

Reference

  • Bertrand Russell, “The Philosophy of Logical Atomism”, pp. 35–155 in The Philosophy of Logical Atomism, edited with an introduction by David Pears, Open Court, La Salle, IL, 1985.  First published 1918.

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Higher Order Sign Relations • 5

Re: Higher Order Sign Relations • 4
Re: Conceptual GraphsGary Zhu

GZ:
Is there any good contemporary reading of Peirce & James that you recommend?  Their original works have been quite challenging for me.

Dear Gary,

As fortune would have it, I haven’t found much to recommend in the secondary literature on Peirce over the last couple of decades.  Most of it looks bent on assimilating Peirce to the conventional wits of analytic and continental philosophy.  As a result, I hew pretty close to Peirce himself in my current reading.  You could try the two volumes of the Essential Peirce for general orientation, if a trifle light on the math side of Peirce.

The last contemporary work I read with anything like the spirit of Peirce about it would probably be Sowa’s Conceptual Structures, so try that if you haven’t already.  Still worth reading are Pragmatism by William James and How We Think by John Dewey.  James and Dewey lacked the mathematical perspective needed to take in Peirce’s full scope and Dewey was a little slow getting up to speed with Peirce’s message but he kept at it and had the benefit of living long enough to become an able expositor of pragmatic and scientific ways.  Plus he understood people and society far better than Peirce ever did.

There are a few references at the end of the following paper.

  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  ArchiveJournal.  Online (doc) (pdf).

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