Changes

{{DISPLAYTITLE:Prospects For Inquiry Driven Systems}}

{{DISPLAYTITLE:Prospects For Inquiry Driven Systems}}

'''Author's Note.'''  The initial portion of this essay is the "Interest Statement" that I submitted as a part of my application to graduate school in the Systems Engineering doctoral program at Oakland University, Rochester, Michigan in September 1992.

'''Author's Note.'''  The initial portion of this essay is the ''Interest Statement'' that I submitted as a part of my application to graduate school in the Systems Engineering doctoral program at Oakland University, Rochester, Michigan in September 1992.

<p><br><font size="4">'''Systems Engineering : Interest Statement'''</font><br>

<p><br><font size="4">'''Systems Engineering : Interest Statement'''</font><br>

This inquiry is guided by two questions that express themselves in many different guises.  In their most laconic and provocative style, self-referent but not purely so, they typically bring a person to ask:

This inquiry is guided by two questions that express themselves in many different guises.  In their most laconic and provocative style, self-referent but not purely so, they typically bring a person to ask:

{| align="center" cellpadding="6" width="90%"

{| align="center" cellpadding="4" width="90%"

| '''&bull;''' ''Why am I asking this question?''

| valign="top" width="4" | '''&bull;'''

| ''Why am I asking this question?''

|-

|-

| '''&bull;''' ''How will I answer this question?''

| valign="top" width="4" | '''&bull;'''

| ''How will I answer this question?''

|}

|}

Cast in with a pool of other questions these two often act as efficient catalysts of the inquiry process, precipitating and organizing what results.  Expanded into general terms these queries become tantamount to asking:

Cast in with a pool of other questions these two often act as efficient catalysts of the inquiry process, precipitating and organizing what results.  Expanded into general terms these queries become tantamount to asking:

:* ''What accumulated funds and immediate series of experiences lead up to the moment of surprise that causes the asking of a question?''

 

:* ''What operational resources and planned sequences of actions lead on to the moment of solution that allows the ending of a problem?''

| ''What accumulated funds and immediate series of experiences lead up to the moment of surprise that causes the asking of a question?''

| ''What operational resources and planned sequences of actions lead on to the moment of solution that allows the ending of a problem?''

Phrased in systematic terms, they ask yet again:

Phrased in systematic terms, they ask yet again:

:* ''What capacity enables a system to exist in states of question?''

 

:* ''What competence enables a system to exit from its problem states?''

| ''What capacity enables a system to exist in states of question?''

| ''What competence enables a system to exit from its problem states?''

====1.1.1.  Systematic Inquiry====

====1.1.1.  Systematic Inquiry====

It is a classic catch, whose pattern was traced out long ago in the paradox of Plato's ''Meno''.  Discussion of this dialogue and of the task it sets for AI, cognitive science, education, including the design of intelligent tutoring systems, can be found in (H. Gardner, 1985), (Chomsky, 1965, '72, '75, '80, '86), (Fodor, 1975, 1983), (Piattelli-Palmarini, 1980), and in (Collins & Stevens, 1991).  Though it appears to mask a legion of diversions, this text will present itself at least twice more in the current engagement, both on the horizon and at the gates of the project to fathom and to build intelligent systems.  Therefore, it is worth recalling how this inquiry begins.  The interlocutor Meno asks:

It is a classic catch, whose pattern was traced out long ago in the paradox of Plato's ''Meno''.  Discussion of this dialogue and of the task it sets for AI, cognitive science, education, including the design of intelligent tutoring systems, can be found in (H. Gardner, 1985), (Chomsky, 1965, '72, '75, '80, '86), (Fodor, 1975, 1983), (Piattelli-Palmarini, 1980), and in (Collins & Stevens, 1991).  Though it appears to mask a legion of diversions, this text will present itself at least twice more in the current engagement, both on the horizon and at the gates of the project to fathom and to build intelligent systems.  Therefore, it is worth recalling how this inquiry begins.  The interlocutor Meno asks:

{| align="center" cellpadding="8" width="90%" <!--QUOTE-->

{| align="center" cellpadding="6" width="90%" <!--QUOTE-->

|

|

<p>Can you tell me, Socrates, whether virtue can be taught, or is acquired by practice, not teaching?  Or if neither by practice nor by learning, whether it comes to mankind by nature or in some other way?  (Plato, ''Meno'', p. 265).</p>

<p>Can you tell me, Socrates, whether virtue can be taught, or is acquired by practice, not teaching?  Or if neither by practice nor by learning, whether it comes to mankind by nature or in some other way?  (Plato, ''Meno'', p. 265).</p>

The primary factorization is typically only the first in a series of analytic decompositions that are needed to fully describe a complex domain of phenomena.  The question about proper factorization that this discussion has been at pains to point out becomes compounded into a question about the reality of all the various distinctions of analytic order.  Do the postulated levels really exist in nature, or do they arise only as the artifacts of our attempts to mine the ore of nature?  An early appreciation of the hypothetical character of these distinctions and the post hoc manner of their validation is recorded in (Chomsky, 1975, p. 100).

The primary factorization is typically only the first in a series of analytic decompositions that are needed to fully describe a complex domain of phenomena.  The question about proper factorization that this discussion has been at pains to point out becomes compounded into a question about the reality of all the various distinctions of analytic order.  Do the postulated levels really exist in nature, or do they arise only as the artifacts of our attempts to mine the ore of nature?  An early appreciation of the hypothetical character of these distinctions and the post hoc manner of their validation is recorded in (Chomsky, 1975, p. 100).

{| align="center" cellpadding="8" width="90%" <!--QUOTE-->

{| align="center" cellpadding="6" width="90%" <!--QUOTE-->

|

|

<p>In linguistic theory, we face the problem of constructing this system of levels in an abstract manner, in such a way that a simple grammar will result when this complex of abstract structures is given an interpretation in actual linguistic material.</p>

<p>In linguistic theory, we face the problem of constructing this system of levels in an abstract manner, in such a way that a simple grammar will result when this complex of abstract structures is given an interpretation in actual linguistic material.</p>

One version of Peirce's sign definition is especially useful for the present purpose.  It establishes for signs a fundamental role in logic and is stated in terms of abstract relational properties that are flexible enough to be interpreted in the materials of dynamic systems.  Peirce gave this definition of signs in his 1902 "Application to the Carnegie Institution":

One version of Peirce's sign definition is especially useful for the present purpose.  It establishes for signs a fundamental role in logic and is stated in terms of abstract relational properties that are flexible enough to be interpreted in the materials of dynamic systems.  Peirce gave this definition of signs in his 1902 "Application to the Carnegie Institution":

{| align="center" cellpadding="8" width="90%" <!--QUOTE-->

{| align="center" cellpadding="6" width="90%" <!--QUOTE-->

|

|

<p>Logic is ''formal semiotic''.  A sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, ''C'', its ''object'', as that in which itself stands to ''C''.  This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time.  (Peirce, NEM 4, 54).</p>

<p>Logic is ''formal semiotic''.  A sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, ''C'', its ''object'', as that in which itself stands to ''C''.  This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time.  (Peirce, NEM 4, 54).</p>

Why have I chosen differential geometry and logic programming to try jamming together?  A clue may be picked up in the quotation below.  When the foundations of that ingenious duplex, AI and cybernetics, were being poured, one who was present placed these words in a cornerstone of the structure (Ashby, 1956, p. 9).

Why have I chosen differential geometry and logic programming to try jamming together?  A clue may be picked up in the quotation below.  When the foundations of that ingenious duplex, AI and cybernetics, were being poured, one who was present placed these words in a cornerstone of the structure (Ashby, 1956, p. 9).

{| align="center" cellpadding="8" width="90%" <!--QUOTE-->

{| align="center" cellpadding="6" width="90%" <!--QUOTE-->

|

|

<p>The most fundamental concept in cybernetics is that of "difference", either that two things are recognisably different or that one thing has changed with time.</p>

<p>The most fundamental concept in cybernetics is that of "difference", either that two things are recognisably different or that one thing has changed with time.</p>

Legend tells us that the primal twins of AI, the strife-born siblings of Goal-Seeking and Hill-Climbing, began to stumble and soon came to grief on certain notorious obstacles.  The typical scenario runs as follows.

Legend tells us that the primal twins of AI, the strife-born siblings of Goal-Seeking and Hill-Climbing, began to stumble and soon came to grief on certain notorious obstacles.  The typical scenario runs as follows.

{| align="center" cellpadding="8" width="90%" <!--QUOTE-->

{| align="center" cellpadding="6" width="90%" <!--QUOTE-->

|

|

<p>At any moment in time the following question is posed:<br>

<p>At any moment in time the following question is posed:<br>

A symbolic calculus is needed to assist our reasoning and computation in the realm of propositions.  With an eye toward efficiency of computing and ease of human use, while preserving both functional and declarative properties of propositions, I have implemented an interpreter and assorted utilities for one such calculus.  The original form of this particular calculus goes back to the logician C.S. Peirce, who is my personal favorite candidate for the grand-uncle of AI.  Among other things, Peirce discovered the logical importance of NAND/NNOR operators (CP 4.12 ff, 4.264 f), (NE 4, ch. 5), inspired early ideas about logic machines (Peirce, 1883), is credited with "the first known effort to apply Boolean algebra to the design of switching circuits" (M. Gardner, p. 116 n), and even speculated on the nature of abstract interpreters and other "Quasi-Minds" (Peirce, CP 4.536, 4.550 ff).

A symbolic calculus is needed to assist our reasoning and computation in the realm of propositions.  With an eye toward efficiency of computing and ease of human use, while preserving both functional and declarative properties of propositions, I have implemented an interpreter and assorted utilities for one such calculus.  The original form of this particular calculus goes back to the logician C.S. Peirce, who is my personal favorite candidate for the grand-uncle of AI.  Among other things, Peirce discovered the logical importance of NAND/NNOR operators (CP 4.12 ff, 4.264 f), (NE 4, ch. 5), inspired early ideas about logic machines (Peirce, 1883), is credited with "the first known effort to apply Boolean algebra to the design of switching circuits" (M. Gardner, p. 116 n), and even speculated on the nature of abstract interpreters and other "Quasi-Minds" (Peirce, CP 4.536, 4.550 ff).

{| align="center" cellpadding="8" width="90%" <!--QUOTE-->

{| align="center" cellpadding="6" width="90%" <!--QUOTE-->

|

|

<p>Thought is not necessarily connected with a brain.  It appears in the work of bees, of crystals, and throughout the purely physical world;  and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there.  (CP 4.551).</p>

<p>Thought is not necessarily connected with a brain.  It appears in the work of bees, of crystals, and throughout the purely physical world;  and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there.  (CP 4.551).</p>