Chapter 7
Measurement, Categorization and Bi-level
Computational Memory
Abstract
A model of human memory and situational logics is being presented in
this book. It is argued that this model may properly ground computational
knowledge management technology through what is an extension of formalism. In 2005 we began to see that pure and applied
mathematics is a type of ontological modeling. Before moving into formalism for duplication and similarly
analysis, in the next two chapters, this chapter will deepen the arguments for
this extension already put forward in previous chapters.
Introduction
We often take for granted the human brain’s evaluation of context,
completeness and inferential consistency. However; in spite of determined effort,
evaluations of this type are not yet made by computational systems. We feel
that the artificial nature to formalism, as well as the mechanical nature of
computer processors, limit the current
generation of computer architecture. As though only one kind of computation
existed, we worship the serial computer, leaving optic computing and quantum
computing aside. The limitation of today's formalism has its effect even
outside of the theory of computing. In previous chapters, we have argued that
this nature of closed formalism has bounded what science can accomplish. As a
result, our artificial intelligence, in spite of costing perhaps a trillion
dollars, is missing most features clearly available to living systems. For
example, living systems understand their environments by acting on the world
and observing the consequences of these acts. Learning is, in this sense,
directly from experience. Computational systems have, as yet, no way to
directly interact with the complex nature of human experience. With optical
computers the story is a different one (Farhat, 1996; 1998).
Humans use natural language to support our understanding of the rich
world we live in. This "knowledge source" differentiates humans from
other biological entities. For humans, learning can be mediated by these
natural "knowledge artifacts". In this sense, language allows humans
to experience in an indirect fashion. We build the same structure for the
computing device using substructural and ultrastructural artifacts, in the form
of symbol systems, to achieve a similar result for the next generation
computing system. These artifacts introduce a type of memory and anticipation
function to the device. From memory and anticipation come an internal language
and then the steady states produced by a system image when confronted by
external stimulus.
In fact, natural language can be seen as one form of human cultural
knowledge. In the sense expressed by the philosopher of science, Karl Popper;
language is one of the artifacts that captures and preserves social knowledge
of the world, externalizing personal knowledge and creating a common means to
communicate between individuals. Though this is true, the individual words and
sentences are not the container of consciousness. They are content that are used
by the brain system to manage individual perceptions. This distinction between
content and awareness has suggested the possibility that computational systems
can be designed to understand its own form of natural language, and more
generally a class of cultural artifacts that can even be used outside of
computer science, including having impact on art and architecture. The
computing devices will collectively and individually make a direct and
independent contribution to the social and personal knowledge of humans. To act
on this suggestion, we need not speak about the mechanisms of awareness, but
rather those mechanisms that create the contents of awareness. The machine we
wish to create is not one with awareness, but one with an almost infinite
memory and a means to anticipant.
Given the economic rewards that would be concomitant with emergent
language understanding technology, were it to be available, we can expect
incremental movement towards a hoped for validation of the suggestion that a
new computational architecture will bring new rewards. In this chapter we will
exam the consequences of this possibility and re-describe a proper
computational architecture. The viewpoints presented before in this book are
thus re-presented here so that the reader can have yet another opportunity to
see the reasoning behind the tri-level architecture.
From neuropsychology and neurochemistry we know that the structural
architecture for human reasoning is multi-level. In spite of what the strong
Artificial Intelligence (AI) community will tell us, the evidence from outside
the AI literature cannot be dismissed as uninformed. We have conjectured that
reasoning works through categorical assignments at each of these levels.
Research contained in (Edelman, 1987; Pribram, 1991; Schacter & Tulving,
1994; and Levine, Parks & Prueitt, 1993) is consistent with this conjecture
and reflects how our views fit within an extensive scholarship.
In the development of these views, we have been motivated by the hope
that computers might use a procedure to perform a computational analog to
cognitive production structures, such as those in the biological mechanisms of
human memory. I have been helped along the path to this conjecture through
discussions with many scholars, whom I often think of as the BCN Group (see
Appendix B).
Because of the nature of our discussions, we have invented the term
"stratified categorization" to map out the requirement that the
architecture we develop have a theory of emergence. We have felt that this is a
necessary step towards proper models of the physical processes involved in
perceptual measurement, categorization, and memory. To support the development
of stratified procedures, notation is introduced in this chapter, and in the
preceding two chapters, that allows some discussion of measurement, stratified
categorization, and multi-level memory within a distributed database.
The notation was developed as part of consulting work that I did on an
architecture for the control and storage of information about the content of
text and image collections. The collections are part of over two billion pages
of classified materials residing, in a scattered about fashion, in government
agencies. The notation, through simple as it is, was considered to be overly
complex by the agencies. Thus the formalism that I developed was only partially
adopted in the declassification projects. However, the full use tof the
notation remains the core of how such a massive project could be organized.
The notation is intended to ground the practice of knowledge management
including those aspects that rely on computers and those that do not. The
separation of many of the problems that information systems are asked to
address, into these two components, is vital to understanding what follows.
Defining the Problem
The management of 25 year old government classified materials was never
our primary interest during the period 1995 - 1998. The declassification
problem was one that needed attention due to an Executive Order (EO) that
President Clinton signed in 1995. The BCN Group members realized that, if
addressed completely, the EO could be the impetus for fundamental change in the
nature of knowledge management. However, this impetus must challenge the
traditional view of formalism, logic and computation. Thus the limited adoption
of part of our work, by declassification offices, was an important step forward
- even if only a small one and one made with great reluctance. The notion was
to create the symbol systems for ultrastructure and produce situational logics
that would aid in managing the nation's classified materials.
Two problems characterized the work on declassification. The first was
the resistance of the Directors of the Offices of Declassification to the
notion of declassification, as a first instance. This is still complemented
with a profound incompetence. The second problem has to do with the
undesirability of having a tri-level architecture existing only in the
intelligence community. It was the second problem that lead to the publication
of this book, and to posting of the early manuscript drafts on the web
beginning in 1998.
Since 1998, a more generic problem has caught our interest. This
problem is how to manage the special type of knowledge artifacts that might
come to exist in computers, in the context of personal or corporate knowledge
management. This is where our interest now lay, and out hope that the economics
of tri-level technology will aid in its development and wide spread use. We
feel that the development of personal knowledge management software is where a
contribution can be given to society. Web technologies and virtual information
management systems seems to be the most promising means to implement our
ideals. So in 1998, the BCN Group began to observe the several classes of
Multiple User Environments (MSE) and Multiple User Domains (MUDs) that have
come to exist on the web.
So where are we in 1999? We know that commercial computational
knowledge management requires a foundational theory where system builders can
account for the natural granularity and overlap of passage boundaries in text,
and concepts in the interpretation of text. Beyond this, we need also a theory
of gestures and states, and an abstract (i.e., generalized) notion for state /
gesture pairing. Both of these "features" must to tired to the
tri-level architecture so that the decisions made by workers are encoded into a
systemic language that produces the knowledge management. The foundational
theory has been implemented as a tri-level process in prototypes that where
built using Oracle ConText software to represent the thematic content of text.
Some experimental work has been completed on the results of using the voting
procedure as an adaptive message routing mechanism. However, the experimental
work has not been fully developed due to the considerable costs associated with
software development.
As BCN Group colleagues talked about the generic problem, we agreed
that human interpretation-judgment was an essential feature that we had to
account for. Our extensive review of the literature in cognitive
neuropsychology, human factors, complex systems and Russian applied semiotics
made this clear. In the architecture that we developed, the phenomenon of
interpretation was accounted for by having the substructure of inferential
aggregation fully enumerated and yet left without semantics. Semantics is added
separately from substructural aggregation from user input of judgment, system
image, and external affordance structures related to ultrastructure ad encoded in
category policies (see Appendix A).
Using the prototype we developed, we take it as given that the
descriptive enumeration of the kinds of things that are relevant, to a class of
observations, will naturally separate into three relative levels:
{ substructure, middle, and contextual }
The enumeration of each of these three levels is a proper objective for
knowledge management. This objective establishes the context of knowledge
management technology development and use. Enumeration is observational and not
based on theory.
The observational grounding for our enumeration methods is based on
three important facts. First, empirical observation, by humans, determines a
set of active observables needed to model and control a complex system, over a
specific time period. We assume, however, that the number of observables is
always small. This means that, in order to control the system, the properties
that we must enumerate about middle level entities are small. The second fact
is that the elements in the substructure of a complex system can periodically
be altered radically. This radical substitution of substructural memory store
allows a combination of substructure within context to model the elements of
the middle level. The third empirical observation is that the context is
defined by how middle level entities move around within an ordered ecosystem.
This allows the context to be tokenized in the form of Petri nets, Bayesian
nets, cognitive graphs (Sowa) or other types of graph constructs.
So if we are looking at concepts, then we need a concept taxonomy of
elementary tokens and relationships between tokens. If we are looking at
structural properties of page segments, as the substructural elements of
scanned images of text, then the pages themselves become the middle level and
these middle level elements are placed into the context of the document using
the voting procedure.
Tokenization and binding
Human concepts are, of course, not easily described by tokenization of
any type. However, it is not so difficult to imagine that a specific text, such
as the Constitution of the United States, could be associated to a specific
cognitive graph. The concepts are described one at a time, with due diligence
made to by accurate and complete. Having meet with the pragmatic requirement of
doing useful work we realized, as is often the case, that a good effort will
produce reasonable value. Various representational methods exist. For example,
if we use knowledge engineering methodology, each concept would be related to a
location, or node, in the graph and the important relationships between the
concepts would be designated by relationships between graph locations.
As an exercise, we imagine the mental state of a Constitutional
scholar. We can imagine the scholar thinking about concepts brought forth by
the interpretation of text. However, the full situation is not so simple, since
we must mix notions of mental states (which require neuropsychology to
discuss), cognitive graphs (which require natural language understanding tools
and cognitive science to discuss), and deductive logic (which is used in
artificial intelligence).
We can immediately see that the granularity of the mental state is not
so easy to delineate, nor are the boundaries of concepts defined by crisp set
theory. So how can we proceed? Our good efforts have given us some value, but
the results are limited somehow. Again, the answer seems to be related to the
nature of interpretation and emergence and the theorems, by Godel, Church and
others, on completeness and consistency.
Continuing with our example, the Constitution can be consistently
interpreted by assuming a specific point of view. Within any single view, one
expects inferential consistency; however, one should also expect that the
"largest" cognitive graph of the Constitution subsumes all of these
views. In this way, all points of view are represented in a single cognitive
graph, which is a virtual cognitive space containing symbolic reference to all
of its possible interpretants.
It is reasonable to assume that this virtual space can have no
"preferred" assignment of meaningfulness, since meaningfulness is
generally regarded as a reduction of possibility to a single point of view. A
single point of view has an implied situational logic that holds the reasoning
together. Reasoning is about consequences in a world view and thus is bound
together with any assignment of meaningfulness.
The binding, then, of meaningfulness into a otherwise not-bound bag of
substructural elements is in the context that is supplied by the third
‘contextual’ level. Perhaps the binding of substructure and context occurs in
the special circumstances coincident with the emergence of a mental image. This
is clearly consistent with our understanding of the formation of chemical
compounds from bags of atoms. Chemical production processes in our environment
supply the context and the atoms supply the material.
In the human brain, global consistency is likely "sought"
through local phase coherence in electromagnetic phenomenon in dendritic trees
as well as through intersystem modulation and adaptive (evolutionary) resonance
(Pribram, 1971; 1991; Grossberg, 1972a; 1972b). In biological neural systems,
resonance works through structural invariance and reentrant signaling between
amygdala and hypocampus, cerebellum and associational cortex, hypocampus and
frontal lobes, etc. Thus, it is reasonable to suppose that situational logics
must account for compartmentalized coherence and the emergence of invariant
forms of behavior.
In the tri-level architecture, context, coherence and completeness must
have proper roles in assembling a computational projection from a large
"situational-less" virtual cognitive type structure. One suspects
that the assignment should "project" onto specific cognitive
structures an interpretation that is appropriate to the situation. But, it
seems clear that, this projection must follow some distributed set of rules
that accounts for these roles of context, coherence and completeness. This is
indeed a very difficult problem, but one that is automatically solved each time
any human reads a book or becomes involved in a conversation.
Methodology
Using the tri-level architecture, universal (aggregated substructural
compounds) semantic spaces can be built without fixed situational evaluation.
Truth evaluation about situational aspects can be separated from an underlying
representation of the components of prototypical concepts. Truth evaluation,
about properties of aggregated constraints, can be distributed and will allow
real time human perturbations of the aggregation rules. So, in a fashion that
is similar to human implicit memory, the situational evaluation becomes
emergent in real time. The mechanisms of this emergence have to be explained as
the results of the voting procedure and the related management of
categorization. This explanation begins with the architectural descriptions in
Chapter 8. (editor's note; this chapter is to be expanded from it's 4/26/99
length of four pages.)
Component representation, in our architecture, allows one to address
the need for pattern completion and inference. These features have important
consequences. In real contexts, the nature of things change, and the completion
and inference must stayed toned to these changes. Perhaps it is also true that
only a little detail may be known about the nature of the components, even as
they change. The Mill’s logic introduced in Chapter 9 allows a part-to-whole
study of relationships between emergent situations, of a specific class, and the
components that are partially known to make up the situation. Pattern
completion and inference, then, occurs into the prototypes of situations. This
is as it should be, for logic is the study of how thoughts "follows"
and thoughts are complex natural processes.
The information management systems produce representations of patterns
in the form of database records, indices of database structures, case logic,
and stored query elements. In some cases, either Bayesian (statistical)
analysis or AI produces some additional organization to the data structures. In
rare cases, the Information Technology architecture supports a model of content
which serves as a model for concept identification and retrieval by concept. It
is via this model that one can use adaptive technology, including the use of
event profiles.
The tri-level architecture identifies the mental image as a projection
from a virtual cognitive space. The space is virtual since it exists only in
the sense of possibility that are emergent from the memory substructure when
the memory is activated in the temporal domain. The cognitive space is a model
of the past, when mixed with anticipation. It is not about the present moment;
since the present moment brings it’s own nature into that mix. But situational
interpretations of cognitive substructures are clearly composed based on
statistical profiles, of some sort, derived from past experience. In natural
complex systems, the prototypes are well represented as statistical artifacts
that can act in a formative fashion in a present moment. The assembly and
binding process is distributed by nature across many instances in slightly
different circumstances. This temporally distributed nature allows the
formative character of the prototype to be instranciated. The period of time
over which the distribution is made allows a statistical representation, as
well as aligns the metabolic or ecological process into well established, but
softly indeterminate, paths within processes that are well represented as
switching network (Kauffman, 1993; Edelman, 1989).
Following this line of thought, in the voting procedure, the election
of category membership is distributed. The process is also algorithmic and thus
perturbation of the voting may allow appropriate contextual interpretation of
some uniqueness about the present situation, where meaningfulness is found.
This perturbation allows the injection of intentionality, for example from the
user during decisions.
Context also involves a degree of expectation. For the tri-level
architecture this presents a problem, since expectation must be built up over a
long period of time. But expectations about the possibilities of the future are
not to be explained in any simple way. Expectations must account for the
ecological circuits that treat the individual as one of many interacting
agents, that is to say as an atom of a particular type. Business process
modeling is generally about an enumeration of client and production life cycles
as defined in a modle of the company's business ecosystem.
In practice, circuit analysis does produce interesting, but fixed and
static, cognitive spaces defined within a situational context. This may be
partially useful in business process modeling, but it is not sufficient for
text understanding. However, using the notation in the next two chapters, one
can add to this static representational space by having available a data
structure for encoding substructural valance (see also Chapter 8). The
emergence of meaning is then via a combination, or aggregation, process, in
context. Procedurally defined logical entailment, in the form of rules and data
structures, is then brought to bear from various types of situational inference
and within a logic produced to express interpretations.
The voting procedures combine some surface elements of QAT with the
deep features of the connectionist architectures. These procedures synthesize
local rules with global rules to produce a stratified categorization policy for
represented objects. The categorizations form a collection in which the
"cause" of the category structure can be assumed to be dynamic. This
non-stationary feature is the primary one that we are exploring in this chapter
and which leads to our definition of "semiotically open sets". In
particular, the dynamic nature of these category policies will be seen in the
way we develop out some elementary notions from topological logic. First we
need to deconstruct a bit of logic.
The QAT
languages
The QAT languages
form a subsumptive relationship:
Loi Ì Li Ì Le Ì L’e Ì L’’e .
Various types of
evaluation functions can be triggered only during the extension of the second
internal language Li to the first external language Le
. It is at this point of extension that we introduce the non- von Neumann
elements in two ways. First is by opening up the sequence of computations to
user input as a perturbation of membership rules. The second is be considering
elements of optical and quantum computing (a subject that is not discussed in
this book). As already mentioned, in standard QAT this assignment of evaluation
is via a multi-valued logic on a set of hypothesis that are defined in Li.
The multiple values are necessary to encode judgments about plausibility and
completeness.
QAT separates the
formal treatment of logical atoms, in Loi, from
both generalization of atoms and formation of compound statements, in Li, and evaluation of
conjectures, in Le. By using the Russian QAT languages in
this way, we have a formal means to separate the atomic structure of semantic graphs
from various distinct regimes of situational evaluation. For example, a
conservative scholar’s interpretations will likely define some part of a
cognitive graph that can be judged to be contradictory to a liberal scholar’s
interpretive viewpoint. Thus different parts of the cognitive graph and
different sets of evaluation rules would be involved in the two
interpretations. The two sets of atoms and two sets of evaluation functions
lead to different inferences.
The results of the
interpretive act are consequent to the structural relationships between atomic
elements, in Loi; but subject to the evaluation
that occurs in Le. In spite of the difficulty of situational
methodology, defining quasi-formal relationships between scholarly view points
allow the substructures of an emergent cognitive graph to serve as a
situational language about mental states, thus providing the necessary parallel
between cognitive science and the stratified computing architecture.
Our atoms and
inference rules
In our system, elementary
fact-like statements are given logical evaluations based on where a passage has
been placed in a text collection. Generic conjecture-like statements are also
given a computed evaluation based on the distribution of category placements.
This computed evaluation is a deduction of truth value given specific
hypothesis and assumptions about facts.
In the Russian form
of QAT, deductive chains are carried out using, as logical compounds, the
semi-lattice of subsets of substructures that "sign" or represent
causes of situations. These substructures can be formed from thematic analysis
of natural language, using any one of several commercial systems.
For example, one
class of deductive chains identify Standard Query Language (SQL) statements
over the set of themes and the Boolean operators. We feel that the concept of
query can be expanded on through the use of situational logic and distributed
processing. For example, QAT defined "blocks" and ‘covers" are
derived as a general means to optimize deductive chains. For us, a block
embodies the cumulative effect of negative knowledge in extended Mill’s logic,
and a cover is a condition where so called minimal intersections occur
in every representation of object instance.
The two notions of
cover and block are basically notions that are topological and logical
respectively, in nature. However, the complete implementation of block and
cover methods from the QAT deductive core requires a more advanced
understanding of Russian QAT than we have yet managed, or at least more than
what I can write down at this time.
In place of these
deductive chains we use a simpler set of one step declarative statements of the
form:
Fact like
statements:
·
theme
ti is an element of the representational set Tk
for a passage.
·
theme
ti is an element of the representational set T*k
for a category.
·
document
di was placed into category q during a training period.
Conjecture like
statements:
·
the
most representative set of minimal intersections, mi, of object
representational sets shared by category g and category r is {m1, .
. . , mn }
·
the
most representative set of meaningful intersections , mi, shared by
category g and category r is {m1, . . . , mn}
·
the
set of meaningful intersections, mi, unique to category g is {m1,
. . . , mn }
These statements
are described by and are evaluated "locally" based on
representational systems derived from past examples.
The general
framework for specifying evaluation functions based on these statements is the
Process Compartment Hypothesis, PCH (Prueitt, 1995; Chapter 1) Each evaluation
is modeled as an emergent "compartment", where the compartment is
formed through an aggregation of basic elements into an interpretant of the
theme representation as one belonging to the categories.
Using the two types
of evaluation functions, a voting procedure may designate category membership
and relationships between categories that were not defined in the substructures
of the basic elements. The relationships are distributed and emergent
properties of the voting. It may be that the category relationships are
implicit, not explicit, in the natures of the substructural elements. However,
user perturbation of the aggregation process may be a cause of emergent
relationships that are not predicted from substructural properties.
Due to either new
knowledge of fundamental changes in the target of investigation, it is possible
that new observables will be introduced and that old observables modified or
removed. This possibility is reflected in a dynamic reconfiguration of the category
policy, as discussed shortly. The last sections of this chapter provides the
proper notation for discussing this reconfiguration of category policy.
To motivate this
issue a bit more, we point out again that context is situational and this means
that observables should be relative. Using the conjectures of the PCH, the new
observables can be recognized automatically and updates to category
representations, substructure representations and computed conjectures (about
category assignments), can be made while leaving open the process.
Such updates will
often lead to non-monotonic effects. So in commercial knowledge management
implementation, change management principles should be carefully employed in
order to not produce community reactions to the nature of change itself.
Moreover, the context itself may change over time and thus the old observables
may no longer be valid. Re-measurement and change management is thus critical.
Primacy of
measurement
In biological
systems, the measurement process is more primitive than perception. This
establishes an important parallel to formal logic. In logical systems the
measurement process is often involved in the formation of axioms and inference
rules, and forgotten afterwards. The same is true for the scientific awareness
about the issue of biological measurement, and outside of a small literature
the measurement problem is completely ignored. Because the logical treatment of
non-static measurement is so difficult, we need some understanding of now
biology handles the measurement problem.
Our intuition tells
us that the human brain recomputes the full set of observables as a matter of
habit. However, we must state that this intuition depends on an analogy between
cognitive and algorithmic deductions. Self and system image is a key notion
within this analogy that will be developed elsewhere (Prueitt, 1987).
A "self
image", of concept of self, provides stability to human psychological
system. So does the memory system. To achieve the same type of stability and
control over our system, we feel that we can use the statistical artifacts that
are stored in a database of substructure representation. But we also allow the
voting to be influenced by external input.
The measurement
process is more primitive than the evaluation of logical atoms. In the
tri-level architecture, we build situational logics after a
"transparent" measurement produces a fresh measure of object and
substructure invariances. Only after this "proper measurement" and
the development of a new situational logic, from the ground up, can we expect
to find complete relevance from the derived axiomatic system.
The way in which
the situational logic is built is not complicated, only complex. By this we
mean that the logic is a consequence of the application of the voting
procedure, which when written down is only three pages long. The voting
procedure itself is distributed and, in our definition of complexity, complex
if it has emergent features. The linkage between the elements of the category
policy is emergent and is how one looks at the issue of reconfiguration of
policy. Thus the voting procedure is complex, but not complicated.
The parallel to
human mental induction
Our immediate
purpose is to describe how one can take some set of signs referent to
substructural invariants and impose a situational deductive apparatus that
produces results similar to conceptual emergence.
This is not
merely the "open systems" problem of encoding the non-monotonicity of
situational inference in a deductive logic, but an open systems requirement for
new situational logic every time the relevant set of observables change.
Russian QAT treats
this problem in a unique way. It was realized that inferential non-monotonicity
is essentially a property of the evaluation functions and these do not get
introduced until after the measurement process has build fundamental
observables and an unevaluated notation is available. Thus a great deal of
formal symbol manipulation can be done on sets of basic symbols without asking
whether or not something is "true" or not. For example, the
manipulation can be in probability spaces, or it can occur as an evolutionary
computation.
The relationship
between things can be gauged at the substructural level to produce something
akin to the atomic periodic table in chemistry. Probability distributions can
be built, as is so often done in the methods of proprietary commercial full
text retrieval systems, and thus used with Baysian analysis to produce a weak
form of inference. The strong form of inference works from an encoding of
tokens that mark the presence or absence of properties in middle level
entities. This presumably must use something like the way we have represented
the completion of Mill’s logic cannons in Chapter 8. This strong form of
inference is "cross level" and thus complex.
Elemental
notions for topological logic
Classical set
theory assumes a fixed set membership rule. Fixed set membership rules cannot
be powerful enough to model natural complex systems over time periods in which
fundamental changes in causation occur. It can not be so due to arguments that
are best put forth in the work of the theoretical biologist Robert Rosen
(1985), and the theoretical physicist Roger Penrose (1993).
The observables that
are needed to describe, control or merely model natural complex system are not
static. Thus a primary distinction is made between complex and Newtonian
systems, in which the observables are always reducible to mass, energy and
momentum. So we need to have a way of talking about the class of observables
that are relevant to a specific investigation or observation of a situation. I
have coined the phrase "semiotically open set" to assist in our
discussion
Let us again
consider some notation. We have defined an semiotically open set to be of the
form:
{ e1 , e2 , . . . , en
, Ào }
where the special
symbol Ào
has the property of adding, deleting or modifying other elements of the set,
and ei is an observable, for i = 1, . . . , n.
We know that the
set of observables must be considered as an semiotically open set where, the
possibility exists at any time, a new class of states may be measured from this
construct. Conceivably, in the next generation machine human interfaces, the
integer n will be dependent on the situational logic developed by the
conversion of cognitive processes to deductive inference on data structures. In
the voting procedure, n is dependant on the stress between the categorization
policy and the user communities satisfaction with routing and retrieval
outcomes.
Lets see how the
notation works. Suppose, for example, the odd numbered observables where
removed and some of the other observables modified.
{ e1 , e2 , . . . , en
, Ào } à { e2 , e4
, . . . , em , Ào}.
m would be the largest
even index number and
ei à ei
could be a
non-trivial replacement based on similarity measures. Suppose then that three
new observables where added:
{ e2 , e4 , . . . , em
, Ào } à { e2 , e4
, . . . , em , em+1 , em+2 , em+3 ,
Ào }
The exercise above
gives a sense of how category policies would be changed, and how one might
model the categorical aspects of emergent mental images.
In order to catch
fundamental changes in causation and linkage, it is absolutely essential that
we identify the active causes, and properties, in situations through periodic
measurement. Only after proper measurement can we evaluate the meaning of
atoms, and only as meaningfulness is "re-established" does a new
notion of monotonicity reassert itself. This is a "monotonicity of
reasonableness" that is softer and less well defined than we find in the
deductive syllogism of strong AI.
In most cases, we
expect that some regular combination of substructures of graphs in the set of
basic elements will model the interpretant. This provides a great utility, but
one that we must use with an awareness of the non-stationarity of natural
systems.
Other types of
semiotically open sets are useful to our discussion.
The emergence of a
computational interpretant must be open to human interaction, and thus an open
class of computational procedures are required to support computational
emergence of interpretants from a set of basic elements (also an open set.)
These procedures can be selected, declaratively, by a human but must be
executed algorithmically by a computer. The same problem arises that we
addressed in representations. The procedures need to be adaptively constructed
in real time to fit situations. Thus we need a substructure that produces a
semiotically open set of procedures through emergence. In this way, the process
of emergence can be perturbed by human interaction at the point of an
(irreversible) objective decision in real time.
Wavelets, global
analysis, and immune systems
A computer model of
human interaction is likely be in the form of some declarative description of
objectives in interaction with a stratified memory system. It should not be
surprising that the representation of objectives might be managed by
computational architectures based on current experimental neuropsychological
evidence and on theoretical immunology. The model of human interaction, as
conceived by the author, would use a Gabor function to encode wavelet
representations into a temporal span.
Wavelet
representations, when used as retrieval indexes, are computationally efficient.
And wavelets can store the full representation of substructure and binding
elements related to category relationships. Thus a paradigm is defined that
would allow global indexing of the structural and conceptual content of very large
text and image collections.
This use of
wavelets, e.g. as a global index, does introduce some topics that can not be
treated fully at this time. Much needs to be studied if the techniques
introduced in this book are used to build large scale tri-level knowledge
acquisition and management systems. However, even without the experimentation
that is indicated, it seems clear from theoretical argument alone, that a
"computational immune system" might use clonal selection based
methods to produce a model of what is, and is not, in protected knowledge
bases. The same argument suggests a means to produce interactive dynamic
computational segmentation of areas in a traditional knowledge base, such as
the one used by the software product, Oracle ConText.
It is thus natural
that we might talk about conceptual antigens that protect the coherence of
interpreted points of view (Prueitt, unpublished).
The selection of
conceptual antigens might involve deselecting pattern recognizers where the
patterns are the minimal intersections of representational sets. This same set
of minimal intersections could serve as the basis elements of the Gabor
transform for computational knowledge management in parallel with what is
envisioned to occur in brain systems (Pribram, 1991).
Measurement
processes
This section
addresses the measurement problem within a paradigm motivated by models of
brain function.
We propose to
follow the guidelines published in the work of the Russian QAT school, but with
certain modifications to fit the problem of natural language understanding. The
guidelines suggest that, like QAT, an open deductive system could be
constructed to reason about meaning, coherence, and categorization. However,
our theory of categorization provides us a strategy to make real time changes
to some essential data structures. These data structures are then interpreted
and manipulated further by the rules of a symbol system or perhaps an
artificial neural network or evolutionary programming. The guidelines call for
a notion of signs that must be quite general since we wish to account for the
phenomena of human memory and memory’s role in selective attention. Thus part
of the sign system would be distributed and thus implicit in nature. The nature
of the sign system must involve openness to new observables and to the
assignment of meaningfulness by interpretants.
We believe that the
biological model tells us how natural intelligence overcomes certain
limitations seen in formal logic and deductive structures. Using metabolic type
processes, the constructed system of signs supports an awareness system for
interpretation of the invariants of a complex system, either directly or
through the imagery of an intermediate logic composes memory substructures. The
problem of understanding natural language is then taken as a special example of
the problem of understanding complex systems.
To be successful,
the system of signs must be directed at a situational grounding of logic about
the unique characteristics of the object of investigation as well as its
statistical properties. This is to be done using structures that are
constructed episodically in parallel with perceptional measurement, the
reorganization of the substructure of memories, and the dual composition of the
contents of awareness.
Representation
and measurement
The substructure
may have representation in the form of explicit logical atoms and inference
rules, as in the Mill’s logic, or implicit basins of attraction, as in the
connectionist systems. Let us look at some notation again to set our concepts
in a more permanent fashion, and see how far our theory might lead us.
Let O be a
set of interpretations of the perceived signs of an object. If w is a measurement device,
then the collection of pre-experiences, w-1(O), must be regarded
as composed from some theoretical construct consisting of unmeasured states.
The construct is modeled around some theoretical notions about un-measured
quantum mechanical states.
The measurement
process takes, as an object of reference, some ontology of spatial temporal
events and produces a more or less well formed set of structural constraints.
These events are observed as measured invariants. An example of structural
constraints is the valance or other affordance characteristics of elementary
atoms when combined into molecules. A second example is the set of
relationships between locations in a semantic net such as Oracle’s Knowledge
Catalog (OKC) or the cognitive graphics of TextWise Inc. These structural constraints
are computational and are enforced when the database management system indexes
text columns using linguistic analysis.
Using a OKC
linguistic processor, O is regarded as a collection of well delineated
passages or, if passages are not distinct and separated, simple written text or
narrative. The measurement process w is a procedural computation
of the theme phrase representations or, if available, syntagmatic units from
the Oracle Knowledge Catalog. As an aside, OKC was the first "knowledge
representational means" to be used by a voting procedure; however, there
are other commercial taxonomy systems appearing in the market place and these
can also be used with the procedure.
OKC was never able
to deliver to the marketplace a method for situational representation. However,
in the tri-level argumentation, the semantic rules for aggregation of logical
atoms are specific to situational classes. Thus we could improve the
categorical performance of OKC in full text routing tasks.
Using the tri-level
architecture, the object of analysis is assumed to be in a context that comes
from a model of the metabolic processes that use topological logic and lattice
theory . Using QAT-like procedures a class of elemental atoms can, in theory,
always be fully identified within the situational context. First, the set of
subsets of the set of all atoms, called the power set on a universal set,
defines a lattice. Connected and complete substructures of this lattice are
semi-lattices.
These semi-lattices
play an essential role in reducing the combinatorial explosion implicit in a
blind application of Mill’s logic to representational sets. In the tri-level
architecture the use of logic is not blind. QAT multi-valued and non-monotonic
plausible reasoning is used to identify important substructures in this
semi-lattice as related to a set of hypothesis about structural similarity
between events. Similarity and equivalence are then operationally defined via
these hypothesis. Similarity and equivalence are thus treated as generalizations
of the topological notion of closeness. The details of this generalization is
yet to be written out and published.
Aggregation
We feel that
QAT-like procedures might identify and constitutionalize structural constraints
on combinations of atoms. Thus extending the class of evaluation functions that
have been developed via our experimental work on the voting procedure. These
constraints identify aggregations of the substructural, logical, atoms
[Pospelov, 1986, pg 37.] Again, we believe that semiotically open sets of atoms
and rules of semantics, derived from structural constraints plus monotonic and
non-monotonic deductive reasoning, should determine the substance of an
intermediate logic in a context in which these atoms are combined into
representational elements.
The proper
extension of human memory to a machine based database must produce an emergent
situational analysis, where stratified and entangled categories form as
bi-products of computing. In human reasoning, these categories are emergent in
real time when a situation is being interpreted. This emergence is necessary to
handle the novelty and non-stationarity of the natural world, as well as to
constrain the otherwise combinatorial explosion that is faced by standard
expert systems.
Our voting
procedure provide deductive extensions to the inductive capability of a
knowledgeable user. This means that the experience of expert input and iterated
refinement, encoded within the tri-level architecture and intermediate logics,
is made available to users in a natural way.
Generalizing the
model of human memory
In this book, a
correspondence is being discussed between the current generation of models
reported in human memory research literature and some unique developments in
Russian open and situational logics. Chapter 5 attempts to unify these models
in support of computer based management of knowledge artifacts.
The unified model
brings statistical representations of the "components" of the past to
the present moment, and parcels the measured states of the world into a
category policy. Expectation and goal formation brings the anticipation of the
future to this same present moment. The model allow a specification of
mechanisms that are observed to create a decomposition of experience into
minimal invariance that are stored in different regions of the brain and the
recomposition of selected invariance as emergent mental states. Similar
mechanisms are used in our machine version of tri-level deduction corresponding
to human induction and cognition (see Figure 1.)
So how does
emergence come to exist, and what substance is combined together? These
questions have been treated in general within various scientific disciplines.
However, we need to treat the issue of emergence in an applied semiotic
fashion, with an eye on how sign systems might assist, through procedural
means, the autonomous "understanding" of natural language text to the
degree necessary to place passages of text into categories.
Figure 1: The process flow that we take as an accurate model
of human memory formation, storage and use.
Our work has
involved a rather deep situational analysis. We know that the quality of the computational
resources, memory stores and situational logics, affects the placement and the
very definition of the crisp or stratified categories needed for knowledge
management.
So there are three
steps,
1.
the
identification of a set of minimal elements that could indicate causation of
properties, and
2.
the
development of a situational logic that predicts the properties of situations
given a partial or complete list of minimal elements.
3.
the
maintenance of a second order system for changing the intermediate language to
accommodate new information.
The first of these
steps are addressed using a version of bi-level logical argumentation, relating
structure to property of functional whole.
Notation for
Category Policies
Let
C = { C1 , C2 , C3
, . . . , Cm }
be a set of
categories, and
(C1 , C2 , C3
, . . . , Cm)
be an arbitrary
ordering of C indexed by the set of natural numbers i = { 1, 2, 3, . . .
, m }. If C has been defined by a training set, O, where
exemplars from O have been ‘placed" into a category, then C
is regarded as a categorization policy.
As we will see from
the experimental write-up in Prueitt (in progress), a specific placement can be
"crisp" where each exemplar is placed into only one category, or
"stratified" where a set of categories are ordered by placement
preference. This ordering, of a categorization policy, produces an assignment
policy for each exemplar.
Figure 2: Bi-level architecture for categorization using
memory
An ordering of the
category sets is indexed by some permutation of the index set I. For example,
if
C = { C1 , C2 , C3
, C4 }
then
C = ( C4 , C3 , C1
, C2 )
is a stratified placement
policy in which category C4 is the first place assignment,
category C3 is the second place assignment, category C1
is the third place assignment, and category C2 is the fourth
place assignment.
Let Q be a membership function
that forms an assignment policy for an event instance Ok. The
assignment policy may be crisp or stratified. In Figure 2, Q is shown as a composition
of a number of subprocesses, each which we assume can be defined procedurally
or declaratively. The declarative definition is made by direct human judgment
and recorded as a placement of training set event instances. In the procedural
definition, the first process is one which forms a representational set for the
event instance, though some "measurement device". These representational
sets are placed into a data structure, but the procedural details of how this
is done is left open (pending additional experimental work on the
representation problem.)
Q performs a bi-level
integration of two processes, I and S, that are linked together
to provide situational logic based on a set of "observables" produced
by the measurement process w, and organized into category representations in the
data structures of O and substructure representations in the data
structures of V. Two pairs of complementary cross scale phenomena occur
(see Figure 2.) In each case, there is one movement from O to V
as well as one movement from V to O (or into a situational
analysis based on O). In both cases the movement, denoted as g, from O to V
is to construct substructural representations. The movement, g-1, from V to O
is an approximate inverse where a compositional closure, of semantic
entailment, is to be made. Ideally, the search for closure constructively
modifies both substructure representations and category representations.
The movement, g followed by S, will
produce a deductive inference in the form of the assignment policy given a new
event instance. In this case, the decomposition from O into
substructural invariants is one that is specific to the event instance. This
decomposition is followed by deductive inference using S. This
composition is used in parallel with the interpretant I to produced an
assignment of situational meaningfulness during emergence of wholes having
parts that are the substructural invariants. The situational interpretation is
about the assignment policy for this whole.
Generalization
of our voting procedure
This section is
purely theoretical, containing as it does some speculations about how the
voting procedure might be extended.
In our private
discussion and in unpublished work, we have found it necessary to develop the
use of certain terms, such as "situational" and "emergent"
logics, to reflect our need to embody cognitive type processes as computational
procedures. This development of new language is necessary because classical
terms and paradigms are simply not powerful enough to embody most of the
processes thought to be necessary for autonomous text based situational
analysis. It is our intention that this new language use should reflect analogy
shared between the processes involved in natural intelligence and the required
class of computer based algorithms.
The notion of a
second order cybernetics is used to indicate the meta-rules that allow one to
change the set of atoms, the rules of syntax and the rules of semantics within
an axiomatic theory (Pospelov, 1986) Second order cybernetics is developed to
convert various transitions to induction to well defined deductive procedures
as new information is added. The openness of the overall system is controlled
with the rules of this second order system.
The membership
function Q is a complex transform that models the "ontological descent"
from the unmeasured world of phenomenon to a "theory" of knowledge
based on memory of the past experience. We feel that memory is stored at two
levels, one being about the set of emergent wholes, in ecological context, and
the other being about the set of substructural atoms. The descent is
multi-leveled, because the memory in V is about substructural
invariance, whereas the memory in O is about whole objects or whole
categories.
The
"theory" is an axiomatic theory that is extended to a quasi axiomatic
theory by using two sets of internal QAT languages and three sets of external
QAT languages. The languages are formal apparatus used to define algorithms as
well as to provide required explanatory theory regarding new capabilities
related to machine learning, machine understanding and knowledge management.
As noted before,
the notation and the relationships between these languages are:
Loi Ì Li Ì Le Ì L’e Ì L’’e
Our definition of
these five languages is different from those described in Finn (1991). However,
the spirit is the same. The first internal language, Loi
, is a set of basic atomic symbols A, a set of connectives ( Ç, È, -,
), as well as
the set of all well formed statements that can be formed with this set of
logical atoms and this set of connectives. The second internal language, Li
, includes, in addition to the combinatorial span of the first language,
the quantifiers (" , $), the extension of the arithmetic on A to the algebraic notion of
variables, and two specific inference connectives (Þ1 , Þ2 ). These connectives were
derived, by Victor Finn, from the logical cannons of J. S. Mill, see (Finn,
1991; Chapter 9).
In our logic, the
external languages are separated from the internal languages through the notion
of emergence.
Li Ì Le
This follows the
proscription by Finn that the inclusion relation between the second internal
language and the first external language, L e, is
one in which a "naive semantics" is realized in an evaluation of
logical atoms (from Loi ), fact like statements
and generic unevaluated hypothesis produced in L i.
The evaluation of
fact like statements are localized to single statements of the form:
p Þ1 O,
where this is
interpreted as "p is an empirical property of object O",
and
s Þ2 O
where this is
interpreted as "subobject s is an empirical cause of a property of O".
The evaluation
function of the first kind is a local evaluation that is based on known
data derived from a training set. As in standard QAT, the first external
language makes a multi-valued assignment of degree of truth to these fact like
statements, thus identifying facts and providing an evaluation of any
conjectures that have been previously defined in the internal languages. This
evaluations of the first kind are dependant on the data structures in O
and V, as well as rules of deductive inference that are defined in the
second external language.
However, we also
have a second type of evaluation function, I, that is made using the
procedural computations of Voting Procedures. The evaluation function of the
second kind is a global evaluation that distributes evaluations of the
first kind according to modifiable production rules. The evaluation is applied
to a new event instance.
The evaluation of
global hypothesis are conjecture-like statements of the forms:
p Þ1 O,
where this is
interpreted as "p is an inferred property of object O",
and
s Þ2 O
where this is
interpreted as "subobject s is an inferred cause of a property of O".
For the purposes of
text understanding experiments the local evaluations are facts directly derived
from the training set of documents. The global evaluations are facts inferred
about the test set of documents.
The second and
third external QAT languages are used to describe the procedures that support
evaluation functions of the first and second kind (respectively.)
The five QAT
languages are related by set inclusion, but also by an extension of the syntax
of sets to Peircean notions of interpretant and semantics. The second order
cybernetics is defined in the second and third external QAT language, and these
second order languages are used to change the theory of structural constraints
and the semantics as a function of real time information acquisition.
The next chapter
will develop the duplicate detection formalism. This formalism is a first step
in realizing the tri-level architecture.