Theme One Motivation • 4

Re: Laws Of Form DiscussionJB
Re: Ontolog Forum Discussion • (1)
Re: Sys Sci Group Discussion • (1)

Speaking of compression, either my present memory or my mind at the time mushed together two different sorts of 1/f scaling laws under the heading of Zipf’s Law, but the overarching principle here is simply “things that vary inversely to frequency”.  Generally speaking, keeping track of usage frequencies is part and parcel of building efficient codes.

In it’s first application, then, the environment the Learner had to learn was the usage behavior of its user, as given by finite sequences of characters from a finite alphabet that we might as well call words and by finite sequences of those words that we might as well call phrases or sentences.  In other words, the Learner had 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 that gives us a leg up, complexity wise, in Interactive Real Time.

To be continued …

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Theme One Motivation • 3

Re: Laws Of Form DiscussionJB
Re: Ontolog Forum Discussion • (1)
Re: Sys Sci Group Discussion • (1)

All through the 70s and 80s I spent many interesting hours hanging out in John Eulenberg’s Artificial Language Lab at Michigan State.  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 sat in on John’s course in mathematical linguistics, which featured Laws of Form among its readings(!), along with Wall, Chomsky, Jackendoff, and the Unified Science volume by Charles Morris that mentioned Peirce in a favorable light.  I learned Zipf’s Law relating the lengths of codes to their usage frequencies and named the earliest avatar of my Learner XyPh, alluding to Zipf and the Xylem and Phloem of its tree data structures.

To be continued …

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Theme One Motivation • 2

Re: Sys Sci Group Discussion • (1)
Re: Ontolog Forum Discussion • (1)
Re: Laws Of Form Discussions • (1)(2)(3)

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 that tell 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 these two projects proceeded in a parallel series of fits and starts through interwoven summers for several years, until one day it hit me that the Learner, one of whose other names happened to be Index, could be put to work helping with sundry substitution tasks that needed to be done by the Modeler.

So I began to integrate the Learner and the Modeler, at first still working on the two component modules in an alternating manner, but devoting a portion of effort toward the task of 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 mood and programming style, I arrived at basically the same graph-theoretical 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.  That is to say, all the strategies that appeared to be 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 this as a discovery

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Theme One Motivation • 1

Re: Sys Sci Group Discussion • (1)
Re: Ontolog Forum Discussion • (1)
Re: Laws Of Form Discussions • (1)(2)(3)

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

I am thinking of “learning” in the sense of “learning about an environment”, in other words, acquiring information about the nature of an environment and being able to apply that information to some purpose.

Under the heading of “doing logic” I am merely lumping together all the ordinary sorts of practical activities that would probably occur to most people under that name.

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

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Sign Relations, Triadic Relations, Relations • 1

Re: Ontolog Forum Discussion
Re: Peirce List Discussion

To understand how signs work in Peirce’s theory of triadic sign relations, also known as “semiotics”, we have to understand, in order of increasing generality, sign relations, triadic relations, and relations in general, all as conceived in Peirce’s logic of relative terms and the corresponding mathematics of relations.

Toward that understanding, here are versions of articles I long ago contributed to Wikipedia and have more lately developed at a number of other places.

Posted in C.S. Peirce, Inquiry Driven Systems, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , | Leave a comment

Theme One • A Program Of Inquiry : 15

Re: Laws Of Form Discussions • (1)(2)(3)
Re: Peirce List Discussions • (1)(2)(3)(4)
Re: Ontolog Forum Discussion • (1)

An unexpected benefit of cleaning out our basement and putting our belongings in storage has been finding a trove of work I thought had been lost, in a stash of 3½ floppies, no less.  I uploaded a sample to a couple of folders on Google Drive.

The first contains a minimal set of files for running the program.
The second contains the example files mentioned in the User Guide.

Apologies in advance for Theme One being a bare prototype, a “text of concept” sort of program.  The user interface is pre-mouse and very finicky but I, its mother, was able to nurse it along far enough to learn a lot from it, and many are lessons of still timely pertinence to our perennial issues.

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Theme One • A Program Of Inquiry : 14

Re: Ontolog Forum Discussion

As an alternative to piling generalities on generalities, not that there’s anything wrong with that, it also helps to look at issues as they arise in concrete applications.

One of the most concrete applications I ever attempted was the program I worked on all through the 80s that sought to integrate a basic form of inductive (data-driven) learning with a fundamental form of deductive (concept-driven) reasoning.  Having recently begun a fresh attempt to essay all that on my blog I think it might serve our ends to share that here.

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment