[Inquiry] Re: Introduction to Inquiry Driven Systems

[Jon Awbrey]

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INT.  Note 13

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1.7.  The Orbit of Inquiry

The preceding discussion has indicated a few of the properties that are attributed to
inquiry and its agents, and has initiated an analysis of their underlying principles.
Now we engage the task of giving these processes operational definitions within the
framework of mathematical systems theory.

Let us consider the inquiry driven system as described by a set of variables:

   x_1, ..., x_k,  a_1, ..., a_m.

Here, the x_i, for i = 1 to k, are regarded as ordinary state variables
while the a_j, for j = 1 to m, are regarded as variables codifying the
state of knowledge with respect to a variety of issues.  Many of the
parameters a_j will simply echo or anticipate the transient features
of state that are swept out by the x_i variables.  However, in order
for the system to possess a knowledge base that takes a propositional
stance with respect to its own state space, other information variables
a_j will have to be utilized in less direct, that is, more symbolic ways.

The most general term that we can use to describe the informational parameters
a_j is to call them "signs".  These are the syntactic building blocks that go
into constructing the various knowledge bases of the inquiry driven system.
Although these variables can be employed in a simple analogue fashion to
represent information about past, present, or prospective states of the
system, ultimately it becomes necessary for the system to have a formal
syntax of expressions in which logical propositions about states can be
represented and manipulated.  I have implemented one fairly efficient
way of doing this, using only three arbitrary symbols beyond the more
passive arrays that are used to echo the ordinary features of state.

A task that remains for future work is to operationalize a suitable
measure of difference between alternative propositions about the world,
that is, about the state space of the system.  A successful measure will
gauge the differences in objective models and not be overly sensitive to
unimportant variations in syntax.  This means that the first priority of
this measure is to recognize logical equivalence classes of expressions,
responding equally to each of their individual members.  This requirement
brings the investigation back within the fold of logical inquiry.  Along
with finding such a measure of difference I will have to specify how these
differences determine the state transitions of the inquiry driven system.
At this juncture a number of suggestive analogies arise, connecting the
logical, qualitative problem just stated with the questions treated in
differential geometry and geometric dynamics.

Jon Awbrey

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