Directory:Jon Awbrey/Papers/Inquiry Driven Systems/Work Area

Note. The following material was placed after "Discussion of Inquiry" in Draft 10.04 (14 April 2004).

Work Area

=Information Theory

Consider a simple communication channel with the characteristics presented in Table 1.

Table 1.  Channel Characteristics
	Sent	Received	Frequency	Probability
	0	0	f00	p00
	0	1	f01	p01
	1	1	f10	p10
	1	1	f11	p11

==The Sign-Theoretic Approach

The pragmatic theory of signs deals with relationships among worlds and languages and the agents who use languages to deal with worlds.

Attempts to understand inquiry are bound to investigate the ways that reasoning agents use languages to negotiate between their worlds and their minds.  In the process one is constantly running into certain types of three place relationships, in the usual course involving objects in the world, signs in the language, and ideas in the mind.  In the pragmatic study of inquiry, a supporting theory of signs and sign relations springs from recurring encounters with this class of relationships.  In the remainder of this section I will describe the subject matter that the theory of signs is designed to cover, outlining the high points of the topic as they present themselves in practice, that is, from a natural point of view and before we begin to theorize in a serious way.

The theory of signs, as a general study, received considerable development in classical and medieval times, and at the beginning of modern times was identified with logic itself (Locke).  The pragmatic version I apply here was devised by C.S. Peirce in the last century, apparently out of logical considerations alone, but most of the topics he staked out and the issues he raised have been forced on our attention again, as integral concerns of the Information Age.  Under one name or another, the same questions come up whenever we have to deal with the concrete nature of physical signals and symbol systems, as we do in communication systems and information theory, or whenever we have to face a multiplicity of synthetic languages and artificial interpreters and to follow their developmental cycles, as we do in simulation studies and software engineering.  Of course, all of these topics are crucial to work in AI.

The pragmatic theory of signs is concerned with relationships among three domains, called object, sign, and interpretant domains.  The specific relationships in question are called sign relations.  The object domain is any set of things or states we intend to discuss, while the sign domain is the language we use to discuss it.  The interpretant domain is the whole collection of ideas and actions that govern the interplay of signs and objects, completing their meanings in connection with a particular interpreter.  On first impression, the interpretant role seems to demand distinctive traits, an essentially different type of character to play it.  On reflection, however, if we take time to consider the function of interpretation in terms of its practical effects, we can arrive at a better understanding of this domain.  In the pragmatic analysis of sign relations we let the class of signs be construed as broadly as possible, viewing ideas as signs in the mind and actions as significant conduct.  From this perspective the interpretant domain comes to be seen as nothing more than a special class of signs, or even just an alternate role that the same class of signs can play.

===Definitions and Examples of Sign Relations

The theory of signs is a developing subject, and a perfect definition of sign relations is still a matter to be reasoned toward, not yet a point to be argued from with any certainty.  What is available is a large number of concrete examples that ought to fall under the desired concept and a small number of classical descriptions that seem to capture essential aspects of the intended idea.  Therefore, a historical and paradigmatic approach is appropriate here.  What follows is a series of approximations and prototypes that bound the definition of a sign relation from above and below, that is, along general and particular lines.  In the present state of development, whenever we do use a definition of sign relations it will always be a tentative one, assumed for the sake of hypothetical argument, and evaluated for the measure of success it provides in clearing up conceptual problems.

====Aristotle's Definition

Words spoken are symbols or signs of affections or impressions of the soul;  written words are the signs of words spoken.  As writing, so also is speech not the same for all races of men.  But the mental affections themselves, of which these words are primarily signs, are the same for the whole of mankind, as are also the objects of which those affections are representations or likenesses, images, copies.	(Aristotle, De Interp., i.16a4).

====Rainy Day Example

In this narrative we can identify the characters of the sign relation as follows:  coolness is a Sign of the Object rain, and the Interpretant is the thought of the rain's likelihood.  

====Peirce's Definition

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.	(Peirce, NE 4, 54).

====Sunflower Example

On a distant planet, space travellers discover a species of phototropic, flowering plants which they naturally call "sunflowers".  There are two varieties of these plants, whose behavior is distinguished as follows.

Table 2.  Photophilic Behavior
	Object State	Sign State 	Interpretant State
	Sun East (0)	Face East (0)	Face East (0)
	Sun West (1)	Face West (1)	Face West (1)

Table 3.  Photophobic Behavior
	Object State	Sign State 	Interpretant State
	Sun East (0)	Face West (1)	Face West (1)
	Sun West (1)	Face East (0)	Face East (0)

Table 4.  Phototropic Sign Relation "S"
	Object State	Sign State 	Interpretant State
	0	0	0
	0	1	1
	1	0	0
	1	1	1

Table 5.  Dyadic Projections of Sign Relation "S"
	P = Proj12(S)	Q = Proj13(S)	R = Proj23(S)
	os	oi	si
	00	00	00
	01	01	11
	10	10	00
	11	11	11

===Sign Relations and Interpretive Systems

I have said that the purpose of inquiry is to reduce doubt and lead to a state of certainty.  If one asks the questions "doubt about what?" or "certainty for whom?" then one has adopted the attitude toward inquiry that is reflected in the theory of signs.  This approach to inquiry takes up the question:  "Who is trading doubt for belief about what?"  The "who" and "what" in question are called the agent and the object of the inquiry, respectively.

Information theory allows us to talk about processes that reduce uncertainty, and this gives us hope that its concepts may be useful in discussing inquiry.  In looking toward components of inquiry that can be supported by effective computational procedures we need to inquire further into the conditions "whether" and the precise means "how" inquiry is made possible.

Bringing all these questions together, a computational systems theory of inquiry is required to ask "what" means "what" to "whom", and it must examine "how" and even "whether" a sign means anything at all.  The pragmatic theory of signs is being proposed to address these tasks, extending in support of information theory a concrete treatment of purpose, agency, method, and context in the particular activities that reduce doubt.

The theory of signs is not an easy subject to discuss, given that I must use signs to do so.  In order to discuss a sign relation I need to have signs for objects, signs for ideas, and signs for signs, involving myself in additional sign relations that extend beyond the sign relation in question.  To avoid an infinite regress, the instrumental sign relations I employ in my study had better be less problematic than the objective sign relations I examine in the process.  Thus, we study a sought after sign relation by clearing a space amidst all the signs about it, using this as a focus and resting place to trace its character and motivation, to note the structure and dynamics of what and how it signs.

As we formalize our study of sign relations a number of issues arise that are potential sources of confusion.  In real life examples of sign relations neither the objects nor the ideas are things that can appear "on the page", as it were, in the medium of signs.  They can only be represented there.  Of course, the particular sign relation we are attempting to study is in itself one such representation, but in order to reflect on it analytically we need a modicum of auxiliary language that is independent of the sign relation being examined.  Often this distinction, between the language under formal investigation and the language used informally in the process, is described as a difference between object language and meta language.

The pragmatic theory of signs, in a deliberate variation from common practice, does not require us to draw the distinction between object language and meta language is an absolute way, nor is it necessary to extend its line globally to divide all regions of language into exclusive camps of a type hierarchy.  The difference between the formula in the foreground and the dialect in the background is a purely local and transient distinction, expressing informal properties of our changing outlook and momentary standpoint.  What is focal and what is global may vary as inquiry proceeds and even change places with each other.  Pragmatic inquiry does not demand a foundation of absolutely certain propositions to build on, but only needs a provision of meaningful propositions to live on.

A number of issues arise as we try to advance our casual discussions of sign relations toward giving a more formal account of themselves.

As we attempt to advance from informal discussions of sign relations to more analytic accounts, ...

When we focus on a particular sign relation, we employ our attention to mark its elements in a special way, setting the focal sign relation in relief against the background of the global sign relation in which it remains embedded.

Let us now try to formalize the study of sign relations in terms of set theoretic and system theoretic models.

The theory of signs is concerned with a class of three-place relations called sign relations.  Given a sign relation R c A3 = AxAxA, where A is any set, the sets of elements appearing in the successive places of the relation are called the object, sign, and interpretant domains of R, respectively.  We may safely ignore the elements that do not appear in each place, letting O, S, I indicate the successive domains and writing R c OxSxI.  In general, the domains of a sign relation are unrestricted subsets O, S, I of an arbitrary set A.  In practice, various kinds of further constraints are commonly encountered.

Looking toward a system-theoretic underpinning for inquiry leads to the following considerations.  The domains O, S, I are taken to be the state spaces of systems O, S, I, called the object, sign, and interpretant systems.  In this setting, the abstract definition of a sign relation is typically filled out as follows.  To begin with, the object system O is treated as a designated agency or determinate system about which a number of other agents must keep informed.  At this point, there are commonly two choices for how we might picture the action.  These are the paradigms we refer to as (1) the communication system and (2) the interpretive system.

If there is a plurality of agents, of which S and I are two distinct members, then we have the basic set-up of a communication system.  The states of the sender S constitute a set of signals or messages which receive their interpretations in the states of the receiver I.

If the roles of S and I are filled by the same agent, then we have a process of self communication, or a process of interpretation carried out by an agent we call the interpreter.
 
Work Area

==The Sign-Theoretic Approach

We have said that the purpose of inquiry is to reduce doubt and lead to a state of certainty.  The sign-theoretic approach to inquiry addresses the question:  "Who is proceeding from doubt to certainty about what?"  The "who" and "what" in question are called the agent and object of inquiry, respectively.  Information theory allows us to talk about processes that reduce uncertainty, and this gives us hope that its concepts may be useful in discussing inquiry.  The pragmatic theory of signs merely adds to information theory an awareness of context, purpose, and agency in the particular activities that reduce doubt.  Beyond the frame of discourse there always looms the weavers and treaders of the text.

The pragmatic theory of signs is suited for these tasks, as it extends information theory by an explicit mention of context, purpose, and agency in the particular activities that reduce doubt.
In a basic class of examples, S and I are the same set, from which O is disjoint.

If the roles of S and I are filled by the same agent, then we have a process of self communication, or a process of interpretation embodied in a single agent we call an interpreter.

{==Differential Models}
{=====Vector Field and Control System}
{=====Fields of Information and Knowledge}
 
Fragments

The unsettled state at the outset of inquiry is characterized by a high level of uncertainty.  The settled state of knowledge at the end of inquiry is achieved by reducing this uncertainty to a minimum.  But uncertainty is a quality whose measure we can take, finding it within the scope of information theory.  This gives us reason to believe that many properties of inquiry driven systems can be studied in abstraction from the affective qualities of the disharmony which drives them.  To the extent that this is true, inquiry driven systems can be taken as special types of control systems, where the variable sought to be controlled is a measure of uncertainty or entropy affecting the intellectual component of the system.

The relation of signs to the states which give them meaning can range from the purely iconic and indexical to the highly symbolic ends of the scale.  The terms "icon", "index", "symbol", and their derivatives are used to describe the kind of correspondence that exists between a sign variable aj and a state variable xi.

A sign is called an icon of a state variable if it shares some obvious properties with it.  A sign is called an index of a state variable if it exists in a clear causal relationship with it.  Here we find the kinds of signs we usually think of as signals, records of signals, or immediate transforms of signals and records.  For icons and indices, the meaning that signs have for the system can be recognized by a fairly direct step of analog interpretation.

At the symbolic extreme, signs can be arbitrary marks in a codified language.  In this case, the agent of the system is compelled to use an indirect process of conventional interpretation to decode their normative consequences for action.  To a large extent, the inquiry driven system does not merely incorporate an interpretive agent for these codes, but is forced to become an interpreter of the language it uses, leaving the meaning of symbolic expressions to be found in their conceivable effects on the total system's own potential conduct.

Besides the scale of indirectness from icons and indices to fully fledged symbols, there is another dimension of variation in the characters of signs that we need to mention.  The kinds of signs we have in mind can be generated either externally or internally, in other words, either determined as conditions at the interactive boundary of the system or else specified only in relation to other components of the system.

Inquiry begins with a genuine doubt that a person has in earnest, not with a general doubt that a person pretends to have.

Inquiry begins with particular doubts that people honestly have, not with a universal doubt that a person pretends to have.

Certainty is not a condition for the beginning of inquiry but only for its end.  What gets us through in the mean time is not infallible truths but meaningful propositions.

The condition of inquiry is not founded on certain propositions but lives on meaningful propositions.  Otherwise, this inquiry into inquiry would not be possible.

The roots of inquiry are not buried in certainty but live on meaning.

Thus, in order to study a particular sign relation we must clear a patch of space around it in the forest of embedding signs, using what light this avails us to trace its mottled form and motive flight.

Thus, we study our quarry sign relation by clearing a space in the forest of signs about it, using what light this avails to trace its form and motive flight.