Notational Foundation to Future Semantic Science


Paul Stephen Prueitt, PhD





Stratification into layers delineated by time is observed within physical processes.  Metabolic processes, for example are organized within what might be referred to as a layer, separate from the behavioral intentions of the living system.  The language to talk about stratification of processes and the interaction between layers of stratification has been largely missing within our scientific literatures.  A notational foundation is offered as a means to set the stage for developing language of this type. 



Section 1: Our justification for using a stratified model

The tri-level architecture

Actionable intelligence

The Orb representation

Atoms and compounds

Formative event models and stratification

How connections are modeled

Purpose of this work

Section 2: Orb based analysis

Measurement using the word level n-gram

General Framework Theory

Generalized n-grams, frames and scripts

Informational convolution

Simple and Differential Convolution

Localization and Organization Processes

The capture of structure

Cross Scale Transforms




Section 1: Our justification for using a stratified model

Our stratified model uses a process for collapsing occurrences into categories to create persistent data structure and relationships.  Observation leads to structural information about various targets of observation. 

The stratified model is not one that can be modeled by classical mathematics alone.  The model reflects how physical components work together to express real world complex behavior.  The concept of complexity is defined as something that cannot be reduced to algorithms, the so call Rosen complexity. [1]  The point of Rosen’s definition of complexity is that many aspects of natural systems are not modeled using Hilbert-type mathematics.  These aspects include free will, intentionality and the natures of memory and anticipation.

In our view, modern science suggests that natural processes are not truly computational.  In our view there is causation lying outside of any formal model that may govern transitions in any natural system.  In spite of this, a great deal of actual knowledge can be acquired about any natural system.  For example, any natural system depends on the emergence of structural configuration to fulfill functions necessary to that system. 

The concepts about coherence and what is a system are relevant.  In our view, stratification is a means to separate systems from environments.  Stratification is also nested in nature, and this introduces a natural complexity that most people cannot see immediately.  The mix of stratification and nested-ness leads us to talk about a relative stratification, when nested structure has different stratified layers, but that at any time scale one finds the organizational features found in other places, within that time scale, within other nested structures. [2] These organizational layers are encapsulated within organisms, but still share information as if non-locally connected.  In our view this connection is in the natural categories that emerge and reside in the organizational layers. 

One result from this new viewpoint is the tri-level architecture for human-computer interfaces and information management. [3] In the tri-level architecture we develop category and structural knowledge about the invariance across many things (memory), and we develop category and predictive knowledge about global processes that are being driven by emerging signal between complex systems.  [4]  An example of the biological sciences related to emerging signal expression is seen in the science of gene and cell signal pathways.  [5]

A stratification of simulations about the natural processes has to be justified.  One way to justify the stratification of processes is to demonstrate a new information science in the marketplace.  However, the capitalization mechanism of the last part of the twentieth century and the first part of the twenty-first century are controlled by the old information science.  So the capitalization of not only stratification theory, but also of related innovations has not been allowed.  Until capitalization process give the stratified theory a fair test, this justification must examine the limitations to formal advanced mathematics.  In this examination we make the argument that far less is being done on critical economic/environmental/social balances that could be.

In the mainstream of science there are assumptions made regarding the universality of mathematics.  However, the processes involved in human awareness have not been shown to be algorithmic in nature. [6] We have the view that the abstraction and assumptions that science uses, until now, may be missing some essential aspect.  Specifically, the nature and foundation of Hilbert mathematics may not be able to reflect many properties involved in human use of information. 

We will make some conjectures about the nature of non-locality in physical systems.  In making these conjectures, we are suggesting that the limitations in Hilbert mathematics, related to determinism; and the limitations in classical logic, related to inference and induction; and the limitations due to not having a formal theory of non-locality; are all different manifestations of the same limitation.  We will be offering new language that attempts to make the underlying reality clear, and to thus lift the limitation through extension to logic, mathematics and physical science.  The extensions are made via an examination of physical coherence, logical inference and physical systems that have layers of organization (delineated by time scale). 

Is the discussion above relevant to modern computer science and the current mess in information systems?  We make the argument, simply, that yes this discussion is relevant.  First, information as defined in computer science is not the type of “thing” that biologists talk about when they talk about cell signaling of information between various parts of a cell. 

The limitations in Hilbert mathematics are seen when one attempts to understand the interpretative and perceptual acts of humans.  Hilbert mathematics plays a modeling role when one is dealing with engineering and certain categories of physical phenomenon.  As such, ontological modeling has the potential to extend classical mathematics.  The nature of ontological models and a comparison to Hilbert mathematics and classical logic is developed in the “Foundations”. 

The notation that we offer is simple, but implicitly recognizes that the ontological model is incomplete without a human acting in an informed fashion.  The solution may be to create open form formalisms in a specific fashion, using a stratified system of symbols and

The completion of a formative ontological model occurs when a human becomes aware of some information.  The human makes the model into a complex process through the act of interpretation.  This means that the model itself cannot be subject to the types of considerations that are implicit in strongly logical systems, such as the W3C supported description logics. 

Our viewpoint is that these works on description logics, which is mainstream and highly funded, is a variant of artificial intelligence discipline and has moved very far away from ground understanding of natural science. 

We can examine this further.  In classical mathematics completeness and consistency plays a critical role, one that is addressed by pure mathematicians and logicians.  This work forms the core of scientific literatures.  In the mainstream academic disciplines, the work by Godel is marginalized.  Also on the margins is the notion of explanatory coherence.  Underlying the work by Paul Thagard [7] on explanatory coherence is the notion that inference depends on “coherence”.  Such work on explanatory coherence is typically regarded as non-mainstream.  As we move a bit further away from classical formalism we find the modern academic fields of neural networks, genetic algorithmic, connectionism, and evolutionary programming.  These academic disciplines all put some type of intellectual pressure on the concepts of completeness and consistency found in classical mathematics.

The tri-level architecture

It is our viewpoint that the failures in mathematics, and computer science, can be partially accommodated using what we have called “stratified theory”.

The stratified model has two forms

(1)   conceptual and notational and

(2)   implementation as computer processes.   

In the tri-level architecture for computational intelligence, our stratified model motivates the use the co-occurrence of parts of words, words and phrases as indicating functional roles.  A formalization relating the parsing of words by algorithms and co-occurrence patterns is expressed in our notational system.  Parsing finds patterns and sues encoded structural information to produce organization at one level.  Higher order patterns then form from an aggregation of this encoded structural information.  The meaning of these high order patterns is then subject to interpretation.  Over time, the encoding of interpretation, to the degree possible, results in a knowledge base that then can be used to assist in future information gathering and future interpretations. 

We say that certain of the concepts are motivating a notational system.  This notional system is the basis for what we are calling the “.vir” subnet standards.  The “.vir” standards are designed to allow certain types of information structures to pass quickly from one processor to another, within a grid architecture.  The standards also align with basic research on how humans interact with information. 

Stratification gives emergence context.  For example ambiguation/disambiguation addresses issues of complexity directly.  In linguistic systems the points of complexity are where there are specific word relationships that cause interpretation depth.  Interpretation is situational.  Function-structure relationships need ambiguation and disambiguation as part of differential responses based on what is available to respond with and what needs to be accomplished.  At the cell and gene expression levels the function-structure relationships are to be understood using quasi-axiomatic theory and qualitative structure function analysis.  These methodologies are not difficult to follow.  [8]

Computational knowledge representation should take into account an under constraint that allows choices to be made at times when an aggregation of substance is emerging to address a specific function.  For purposes of what is often called “semantic extraction from text”, the representation should balance the limitation of computer technology with human in the loop influence and control. 

In natural settlings the emergence of function from the aggregation of substructure passes through choice points.  At these points, in both time and space, the specifics of environmental conditions, such as the distribution of actual substructural elements, forms a type of negotiation over actual synthesis of function.  It is suggested that during this function-structure negotiation nature builds symmetry inductions and that these symmetry induction produce secondary consequences related to the creation or modification of natural category. 

Actionable intelligence

Actionable intelligence depends on organizational information to assists in decision-making.  We developed the nine-step actionable intelligence process model (Figure 1) in 2002, by modifying a seven-step actionable intelligence process model that was widely discussed, and used, in the American intelligence community. 

The intelligence community’s seven-step model left out two aspects.  With a structural disconnect between measurement and the formation of natural category, the seven-step model is incomplete. The nine-step actionable intelligence process model is dependant on the development of “under-constrained” ontological models and the active participation of humans in real time synthesis of information.  During the development of a situational model, the participation by humans brings external knowledge into a re-enforcement of the model. 


Figure 1:  The Actionable Intelligence Process Model (AIPM)

To be clear we recognize the value of the classical notions of logic and formal systems.  The classical foundations of logic serve us well, up to a point.  But this foundation is absent a complete understanding of perceptual measurement, and the physical properties related to those physical phenomena.  The emergence of new category and modification of existing category is core to the essence of intelligence. 

A more generalized statement can be made; indicating that the paradigms available to intelligence agencies and the department of defense are based on an incomplete analysis about what computer algorithms can do.  The so-called intelligent agents, funded heavily by DARPA, do not have perceptual interfaces to the real world, as do living systems.  Heavy funding invested the contractors and the government in a model that would not work well in most situations. 

The nine steps is a process model.  To instantiate this process model we needed an ontology modeling standard.  In the late 1990s I developed the notion of a referential base.  In a referential base, of informational bits, computational representation of information is treated as being incomplete, and requiring of additional constraints from a measurement of what the information is referring to. 

There are both algorithmic and non-algorithmic processes.  The referential base supports analysis based on a direct and precise instrumentation and measurement of structure in data.  This measurement occurs as part of an instrumented system for mechanical control of environmental systems or for a system designed to represent the concepts being discussed within a community or community of communities. 

We have developed a cyclic process that produces a specific discrete model of concepts being expressed within communities.  The representation is of co-occurrence patterns that, when perceived by a knowledgeable human, provide a clear, complete and consistent perception. 

The model of concepts being expressed involves a model of relationships between classes, objects, and between class:object pairs.  One can see that a large number of enumerated object-to-object relationships can be thought of as one layer of organization to human communicative acts in real time.  The class-to-class relationships can be seen as the essence of how human language is formed and used.  The class to object paring allows information to be encoded about how specific communicative acts, in real time, are building or dissolving categories of meaning as understood commonly by a community of humans involved in communicative acts.

These two processes become integral and situational when humans are involved.  A specific model is produced in a similar fashion as a relational database model, except the data is designed to be stored as simple separate bit structures, as opposed to within a specific fixed schema, thus allowing organizational process to express the data with greater flexibility.  The simple bit-structure is related to two classes of innovations that are integrated in the “.vir” standards, using specific innovations related to a stratification of category formation and the aggregation of semantic primitives into single coherent models. 

Our group holds that discrete analysis, about reality, must involve a sophisticated use of both machine ontology and human based reification cycles.   The machine ontology has to be both very simple and not yet organized into rigid constructions. 

The role of the AIPM in developing proper ontology and reification processes was first seen in the application of referential systems to text understanding.  Our Orb (Ontological referential base) based text analysis involved the measurement of co-occurrence and frequency of terms, phrases and patterns in text.  Using the Orb data constructions, classical techniques from knowledge discovery in text technology were combined with advanced linguistics and ontology services.  The result was that the referential system inventoried meaningful variation in text.  Human annotation was then allowed to annotate the patterns and invariances. 


The Orb representation

Stochastic methods are used to organize information from large data sets.  A huge academic literature exists on this subject, and there are very large funded research programs dedicated to these methods.  Two types of stochastic methods exist to identify linguistic variation closely associated with subject matter indicators.  Latent semantic indexing and probabilistic latent semantic indexing is one type, though these are really quite different.  Hidden Markov Models is the other type.  Regardless of the type of method used, the result can be encoded into a simple notational formalism. 

In 2001, we developed a specific methodology for translating the results from any stochastic methods directly into a set of ordered triples having the form

{ < a, r, b > }

Using this representation, it is really simple to provide rapid computer processes for subject matter retrieval over large data sets. 

The ordered triples can be encoded into computer memory using three hash tables, with the set of first elements, and set of second elements and the set of third elements being made into the hash keys, and the related data being placed into the hash container.  This encoding is discussed below.  However, it is important to note that a slight modification of the hash table moves the technology into an area that seems dominated by the Gruenwald patents on representing the text string as a base 64 number [9].  When this happens we have a key-less hash table and an efficiency change in one to two orders of magnitude.

We enter a mystery and come out understanding something that seems magical in nature.  The magic is two fold.  First the entire information space is easily encoded as a simple low-resolution image file of a few hundred thousand bits.  Second, the search and retrieval function is almost instantaneous due to the holonomic feature discussed by Nan Gelhard and myself.  [10]

The key to understanding critical scalability issues is to see empirically that the size of the set of primitives, the first, second and third elements; is limited by a categorization process that collapses occurrences into operational categories.  From large data sets there is a type of compression of data into structural relationships.  This compression builds categories and after a while all categories are found, unless the data set itself changes. 

In my work the problems related to organization of very large data sets develops an index in the form { < a, r, b > }. Each of these hash tables are ordered using the key-less index, where a point in this finite 3-D Hilbert space corresponds to individual triples.  The index takes on an organization using mathematical operations that are well understood and which do not involve statistical inferences.  A set of categorical definitions and relationships between categories is mapped precisely to a finite 3-D Hilbert space. 

Moreover, the index itself can be separated from the data and further organized into an ontological model about the meaning that the data may have in various contexts.  In this way, ontological models of social discourse can be developed.  The two fold magical qualities are preserved by the social conventions encoded in natural language use.  The same techniques may also, in theory, be applied to various types of data such as data derived from scientific instrumentation.  The point is that the Orb notation condenses the output from the many data mining and data harvesting systems, resulting in a well-specified structure and having certain formal properties related to the discovery of function of what is observed algorithmically.  Orb notation will act like a standard common integration of the acquisition of data structure.  Also, since the result of computational processes is close to a well-specified ontological model, existing ontological models can be used as a pattern recognition system, and for other purposes.  Foundational research on brain and behavior may suggest that actual brain behavior systems may work based on a very similar principle.  [11]

One of these purposes is realized if the ontological model is represented as a Topic Map.  The actionable intelligence cycle, discussed in the previous section, acquires data from databases or from some measurement process.  Humans are able to see organizational structure and to use existing ontological models as well as personal insight to produce quality models of whatever is the target of the cycle. The Topic Map standard is then used to create a well-organized index into information structures, even those structures that were not involved in the initial measurement.  This cycle follows the action-perception cycle found in living interactions with environments.  All data non-interoperability issues never arise. 

The existence of ontological models brings up the question of interfaces between the output of statistically based analysis, linguistic analysis and human annotation of these results.  Using ontological modeling, the computed results are deterministic and can be controlled by a human to achieve a fine resolution over an event space.  In theory, the encoding of co-occurrence leads to a type of scientific investigation of phenomenon that is complex in the Rosen sense.  I have elsewhere talked about Rosen complexity as being a necessary consideration when modeling living systems and do not wish to diverge to far from the initial discussion of the Orb representation.  The point to make is that ontological models, of the type I am describing, can serve in the same role as Hilbert mathematics.  The difference is that Hilbert mathematics does not capture the essential non-algorithmic nature of certain aspects of living systems.  The similarity is that there can be an induction of a well-specified model by a human mind and the externalization of individual observations into that model.  The model can then be shared between members of a scientific community. 

If people act in a way that leads to these types of models and people use such models to communicate structural information, then they act in an objective fashion even if they are concerned with phenomenon that has not had successful Hilbert mathematics modeling. 

The new ontological models also have a reasonable expression within distributed communities.  A co-occurrence measurement phase in the action-perception cycle has a simple encoding mechanism that uses hash tables to encode informational bits.  The bit structure expresses the form (class, object) where the class gets its definition from what is a stochastically defined neighborhood “around” all of the occurrences of the object, and the object gets its definition from a specific occurrence of a neighborhood.  These formal constructions allow the human to add the required complexity to a symbol system through the process of annotation and interpretation. 

In the next section we give a complete set of elementary formal indicators. 



Atoms and compounds

We may define relationships between objects:

< o(j), r, o(i) >

where o(i) and o(j) are objects from a set O = { o(i) | i is over an index set }

We may separately define relationships between classes:

< c(k), r, c(j) >

where c(k) and c(j) are classes from a set C = { c(i) | i is over an index set }.

Classes and objects have relationships related to categorization.  Without imposing any type of classical or modern description logics, these categorical statements can be encoded into the holonomic structure discussed in the previous section.  The non-imposition of logics is part of the removal of formal semantics from the ontological models based on Orbs.  This removal of semantics then allows the real time imposition of “meaning” via human interpretation.  The interpretation is evoked by standard construction Topic Maps acting as a sign system. [12]

Consistent with the stratified organization of categories, we may define relationships between class:object pairs (nodes):

< n(k), r, n(j) >

where n(k) and n(j) are nodes from a set N = { n(i) | i is over an index set }

In addition to the class object distinctions we find it useful to have notation for: 

a set of atomic constructions

A = { a },

and a set of compound constructions

C = { c },


The relationship between atomic construction and compound constructions may be used to reify instance:class information.  It was proposed, starting in the mid 1960s, by the cybernetics school of Pospelov and Finn that a quasi-axiomatic inference apparatus allows the development of structural knowledge about the formative process expressing as function from the aggregation of substructure.  [13]  This work was literally unknown in the US until the Army Research Lab conferences starting in 1994. [14]

My notation allows nesting of structure:function information.  For example, atoms can be represented as class:object pairs.  The atom object is a simple occurrence, but in some nested cases the atom object would be an occurrence of a category.  The atom class is the invariance at the level of organization that is the substrate to the categories in a level of organization one layer above in the nested structure.  This nested structures are self organizing in nature, and also in the stratified ontological structures based on the Orb notation .  The formation of a simple object compound is then shaped by the function required by a complex (living) system.  This compound is then “participatory” in the definition of a category of compounds expressed from the occurrence of class compounds at a lower level of organization. 

My notation is original work that is designed to provide an provable optimal information encoding standard for developing simple Topic Map interfaces to emerging ontological structure based on action-perception cycles involving human to computer interactions. 

The annotation, by humans, of the observed meaning/function of compounds can be derived from empirical analysis similar to the scientific method.  The stratified model allows us to do the bookkeeping about category formation over time and at multiple levels of organization (of the same reality) as expressed in real time.

Orb constructions can, therefore, play the role, in complex control and analysis, that Hilbert mathematics plays in engineering science.


Formative event models and stratification

An interpretive act is involved in human awareness of information.  Of course, computers have no similar function.  An objectively observed correspondence between word co-occurrence and subject matter experienced by humans is essential to design interfaces.

The process in which language is created is seen as part of an ecological process where patterns of co-occurrences come to make sense to a human as part of social conversation or as part of the reading experience. 

Looking at a general and abstract model of mental event formation processes further grounds a theory of process stratification.  The mental event is seen as the central phenomenon that we refer to when we think about the experience of subject matter when text is read.  But the formation of natural language within community occupies a similar important position in the theoretical framework.   The mental event occurs within its own world and is yet is separately influenced by the human community.  The stratification model allow complexity to be part of the model. 

We can use co-occurrence between significant words and make the observation that certain co-occurrence is predictive of subject indicators.  The whole is then regarded as a composition of elements that are abstract representations of occurrence of significant words across multiple instances. 


Figure 2: The graph neighborhood with center at the word “attack’

The net of significant words is expressed as a graph and a topology is developed on this graph with “neighborhoods” having centers on significant words and non-center elements precisely those significant words that are actually co-occurring within the text under study.  The co-occurrence related to each significant word is visualized as this graph neighborhood.

An abstract model of emergence brings one to fundamental physics and to the phenomenon involved in the physical emergence of something.  Obviously this category of phenomenon has been difficult to model formally using Hilbert mathematics.  This issue is discussed well by I. Prigogine in his book, End of Certainty.  Pribram has also developed a certain presentation of what he has called scientific realism, where a underlying theory of thermodynamical structural constraints are involved in the emergence of chemical compounds and in the emergence of field coherence, as a general principle.  In our opinion, Gerald Edelman makes a similar presentation in his book “Neural Darwinism”.

The differential ontology framework is based on this same type of scientific realism.  In differential ontology a “semantic” compound is composed of (co-occurrence) relationships between significant words.  Because these co-occurrence relationships repeat in many contexts, they become identified as an invariant across these multiple occurrences.   A reality, out there, is necessary in order that the invariants have situations in which to aggregate.  This aggregation process is not fully constrained by known natural law, and thus the function of an aggregation is underconstrained. 

The collection of all co-occurrence relationships that includes the center word is treated as a single “subject indicator”.  These neighborhoods can be corrected for words having more than one meaning, and the neighborhoods can be incomplete.  The function of an aggregation of invariances is underconstrained, while at the same time the structure of the aggregation required to fulfill a specific real time function is degenerate in precisely the fashion discussed by Edelman. 

The differential process, in the abstract, can be thought of as a model of event formation.  Using a hypothesis called the process compartment hypothesis, the parallel between a purely algorithmic process and natural processes is exposed (Prueitt, 1995). As a result new computing processes can be developed both as fundamental cognitive science and new computer algorithms. 

Consider the case where atoms are class:object pairs and these pairs are regarded as graph nodes. Relationship between nodes may be derived from class and/or object relationships.  For example consider,

< n(k), r, n(j) >  

if the object in the node n(k) is the object in the node n(j).  In this case the relationship is some type of categorical equivalence.  The two objects may be different, but are regarded by the ontology as being the same. 

A collection of the relationships between nodes can always be rendered as a graph.  The categorical equivalence collapses more than one node into a single node, as illustrated in the figure below. 



Figure 3:  Convolutions over sets of nodes may collapse into a category

In Figure 3, we are illustrating the convolution over three occurrences that are deemed to be within an equivalence class.  This illustration might be particularized if in three cases, a single word stem was co-occurring in specific text.  The convolution would bring these three nodes together as a single representation. 

How connections are modeled

A graph is a set of nodes and connections between some of these.  The set of nodes are indicated, enumerated, as a set { a(i) }.  One can use very elementary constructions from graph theory to encode specific, precise and exact information about any of a number of measurements. 

The knowledge representation problem is challenging. Human sensory and cognitive acuity measures type and differentiation of type in the development of specific knowledge, awareness and anticipation.  But cognitive function does not follow classical logic.  The specific failures of logic seem clear.  Classical logic has not been shown to have the capability to deal effectively with natural function/structure phenomenon. 

Orb analysis produces a single relationship, co-occurrence, r, of two words, a and b, within a certain specified proximity produces the exact and precise measurement “ < a, r, b >”.  A document collection is processed and then visualized.  The result is the Orb, whether represented as a graph or as a set of order triples:

{  < a, r, b >  }

A semantic topology is used to “cover” the subject matter with topological neighborhoods having the center of the neighborhood an element of an upper taxonomy or controlled vocabulary.  Each of the neighborhoods is presented to humans for annotation. 

Before a connection can be made, one needs to have things to connect.  In the Orb notational system, we call these “things” either atoms or compounds.  Again, if we have a theory of relational type, then relational types can be atoms or compounds in a theory of relational type.  But we have only one type of relationship, co-occurrence.  The withholding of any theory of type accomplishes three important results.

1)     Meaning is not assumed to be captured in the precise and exact measurement of word occurrence.  Because it is not assumed to have occurred, one is able to make it clear that the knowledge technology based on Orbs requires active human reification cycles to be properly used

2)     The precise and exact structure of co-occurrence can be restricted to a small number of key terms.  The Orb projection from a largest Orb, where all terms are considered significant, to a smaller and visually accessable Orb is done in a single pass over the Orb structure. 

3)     What is called “mutual induction” is supported. 

In building Orbs we can define algorithms on the simple ASCII text list of ordered triples, or on the graph structure. 

A correspondence is made between a specific class:object pairing and a node.  We should be clear here, that simple co-occurrence does not really depend strongly on naturally occurring class:object structure.  Structural patterns are measured precisely because the co-occurrence structure is there in the text or in the data.  The patterns have to be understood.  Benchmarking on cyber intrusion data demonstrated a fractal compression of data into information structure simply due to the collapse of categories into single constructions.  Fractal compression means two things,

(1)  self-similarity is observed at multiple levels of scale, and

(2)  after an initial period, the rate of growth over the size of the encoding mechanism, an Orb, begins to decrease and becomes very nearly zero after a while

Various implications follow from these two features of fractal compression.  One of these is fractal scalability.  The second is that the identification of event structure can tolerate measurement error and incompleteness. 

The formation of classes has two parts, the structural and the functional.  These parts are kept separate so that human intuition can play in situational judgments, in real time.  The exercise of this judgment when in conjunction with Orb processing is called “mutual-induction”, and creates both a type of inference and work product having a standard form. 

The mechanisms supporting mutual induction bring human tacit knowledge into the work product.  The visual form of the Orb pattern invokes an induction of some type of mental experience. 

Figure 4: Subject Matter Indicator neighborhood within the 1997 – 2003 FCC public rulings

What mutual induction is acting on can be simple, or more complicated depending on the nature of the problem at hand.  

The simple co-occurrence relationship is encoded as a link between two nodes.  Taken alone, a class:object pair may be a node without (necessarily) having any links to any other node.  This happens to be somewhat uninteresting, when compared to a rich theory of semantic type.  We assume that the use of advanced theories of semantic type cannot be accomplished without a knowledgeable and informed human in the loop. 

The connections between terms in language expression are not always best measured from the co-occurrence of terms in text.  But it is difficult to come up with some other way to lay down a basic measurement process that is simpler and yet achieves such a high level of success.  The understanding of text by humans involves most, if not all, of the capacities of the human perceptual and cognitive systems. 

With Orbs, the computer technology works in a precise fashion to create a retrieval of those documents with specific co-occurrence patterns that are visualized in the local subject indicator neighborhood.

Purpose of this work

The development of co-occurrence connections is not ultimately the only objective of our work.  Our objective is to develop a representation of the flow of knowledge within a social system.  This means that the currency of human knowledge exchanges have to be detected, inventoried and then various theories developed that allow one to judge, in an automatic but modifiable fashion, when specific elements of this currency are being expressed. 

The Orb technology simplifies what one attempts to do with text understanding systems.  Humans already have this ability to understand text and to communicate with each other.  What we need is not to “understand the text using machines”, but rather to develop a detection capability that targets patterns in expressions.  These patterns can be found without there being any understanding, claimed or otherwise, by the computer.  Then when the patterns are presented to any user, the meaning is immediate.  Mutual induction occurs and produces a mental event.  The mechanisms involved in the production of this mental event are not exclusive to the computing machine. 

The Orb technology can be embedded into a graphical user interface that supports annotation, various manipulations of data and other features expected from the fully operational software. 

The technologists in our group have developed some techniques for mapping co-occurrence and for reifying, or making human-like, the linguistic variation as types and expressed as visual symbols.   Slightly different methods will be proposed depending on if we are developing a memetic expression detection system or a knowledge management system based on general framework theory.  The methodology for properly developing and using Orbs is discussed in the next section.


Section 2: Orb based analysis

Discrete analysis using Orbs allows organizational process to express class:object data in various ways.  This type of analysis can be done about any phenomenon. 

When the phenomenon is complex, i.e., having a least one non-deterministic state transition; then the encoding of discrete analysis as ontology is a reasonable way to achieve objective representations.  The analysis is localized into a formation of categories and patterns of categories.  Classical text analysis initially involves the measurement of co-occurrence and frequency of patterns in text.  But other methods such as latent semantic indexing and scatter-gather methods can also be used to develop a model of the relevant classes and objects as indicators of concepts and intentions being expressed in text. 

Various work product include the development of broad-term / narrow-term upper subject matter taxonomy and back-of-the-book indexing for subject matter retrieval.  Automated taxonomy generation for un-indexed document repositories was demonstrated in our work on a FCC taxonomy in 2003.  The FCC taxonomy was developed using a topological construction defined on Orb graphs.

All of these methods feed into the simple set theoretical constructions, having the form of a set of syntagmatic units: 

{ < a, r, b > }.

The measurement of term occurrences is a first step but only a first step.  There is an overriding principle.  One uses a specific philosophy that separates structure from function and allows the human to make judgments about function. 


Measurement using the word level n-gram

Measurement by word level n-grams produces an ordered set

A = { ( w(1), w(2),  . . . , w(j), . . . , w(n) ) }

If n is an odd number, then w((n-1)/2) is the center of the n-gram, and two branches of a special type of graph, a tree, can be rendered from this n-gram. 

For example during a word level n-gram measurement process, the sentence with words:

a b c d e f g h

is output as a set of eight 5-grams 

{ (-,-, a,b,c), (-, a,b,c,d), (a,b,c,d,e), (b,c,d,e,f), (c,d,e,f,g), (d,e,f,g,h), (e,f,g,h,-), (f,g,h,-, -) } 

Each of these 5-grams can be used to label a graph, for example the one in Figure 5.

Figure 5: The simple tree developed from a word level 5-gram

One can use the center word as a root node and develop branches with the left part of the n-gram and the right part of the n-gram.  On the other hand, the n-gram can be used to label a single “branch” as in Figure 6.

It is noted that variable length word level n-grams and other methods also produce tree branches.  For example, there are eight 3-grams for the sentence with words:

a b c d e f g h

A word level 3 gram analysis is output as:

{ (-, a,b), (a,b,c), (b,c,d), (c,d,e), (d,e,f), (e,f,g), (f,g,h), (g,h,-,) }

and produces eight small trees.

More general graph constructions can be built using n-grams. 

Figure 6:  A branch developed from a word level 5-gram

In our system we will not use only standard word level n-grams.  A more sophisticated means to produce the graph constructions are used as well.  This means is called generalized n-grams and may use a framework theory (as discussed in the next section).  An additional rule engine can be presence when the co-occurrence of significant words is being determined. 

General Framework Theory

The general Framework (gF) notational system produces a different type of data source than does text.  gF Orbs are defined below. 

The Zachman Framework is a well-known business framework.  Two lesser-known examples of frameworks are the 12-primitive-element Sowa Framework and 18-primitive-element Ballard Framework for knowledge base construction.  These Frameworks are three of many that could be adopted. 

The measurement output from an 18-element framework has the form of a 19 tuple:

< a(0), a(1), a(2), . .  . , a(18) >

where the value of a(0) is set by a pre-process that categorizes the event that the Framework will be used to characterize.  When any of these frameworks are used, one produces a n-tuple where each element may have a class type and a value.  The type is derived from the semantic primitive’s definition.  The user, or some other means, supplies the value. 

Suppose that 100 events have been considered. 

Domain space = { E(i) | i = 1, . . . , 100 }

A prototype Framework Browser, designed in 2002 by OntologyStream Inc, stores the cell values as strings, and inventories these strings into ASCII text.  A key-less hash table management system is used rather than a relational database.  The Browser elicits knowledge from the human clerk and then stores this in a convenient way.  The software is operating system independent and occupies less that 200K of 32 bit computer memory.  The prototype builds gF Orbs and stores this data as independent and editable ACSII files.  As larger data sources are addressed, these independent ASCII files exhibit the nature of fractal compression of data. 

Suppose that a parsing program produces a correlation analysis and results from this analysis is encoded into a “derived” 5 tuple:

< a(0), a’(1), a’(2), a’(3), a’(4) >

where a(0) is the event type and a’(1), . . . , a’(4) are each slot-fillers that minimally sign the cell contents. 

The derivation process involves a reification of the slot-fillers in the context of the framework, and this means that a theory of type may be developed for each slot and a theory of relationship may be develop between various slots. 

In one version of a frame filing process, there is a reduction of a free form of writing to a set of standard fillers for cells.  Over time, the filling of cells is made from a pick list and the pick list is maintained empirically.  In practice, we feel that a community based reconciliation processes is necessary.   There is always a potential requirement to introduce new types of fillers at any moment.  It is easy to imagine a type of “open logic” governing the processes.  When new structure is encountered, a provision is made to adjust the underlying set of atoms and compounds, as well as the rules over which event chemistries are used.

The set of fillers for each framework cell (a cell is called also a slot in script theory in Schank’s theory (1977)) becomes the set of natural-kind that is observed to be the structural components of the event under consideration.  These structural components are the substance of events, such as cyber, memetic or genetic expression and the discoveries of relationships between structural elements are achieved using categoricalAbstraction (cA) and eventChemistry (eC) interfaces. 

The similarity between gF Orbs and full text Orbs is straightforward.  The slots’ functional dependencies are rendered visually in the framework browsers.  In the full text Orbs the co-occurrence of terms are rendered. 

A predictive analysis methodology using cA/eC is also fulfilled in a nice way.  Predictive analysis methodology supports what we call “mutual-induction”, where human and computer processes are entangled in real time data processing.  To restate, we call this Human-centric Information Production (HIP).

Suppose that 100 events have been considered. 

Domain space = { E i | i = 1, . . . , 100 }

In each case, the framework has been filled out through:

·        ·Interactive knowledge elicitation involving human dialog and/or

·        ·Some artificial intelligence process that fills in anticipated cell values using a theory of type related to each framework slot.

The domain space is now described by 500 individual data pieces

{ < a(0), a(1), a(2), . .  . , a(4) >k   | k = 1, . . . , 100  }

where {  a(0) k   | k = 1, . . . , 100  } are the event names, derived by a prior process.

{  a(1) k   | k = 1, . . . , 100  }

are the (1) cell values of the 5 cell matrix that represents the framework, and so on. 

We will use the notation

{  a(i) k   } = {  a(i) k   | k = 1, . . . , 100  },

for a fixed index element i.  The size of the set {  a(i) k   } is less than or equal to 100. 

The reduction in size of these sets is due to the naturally occurring data regularity in specific context.  Remember that the set { 5, 5 } is equal to the set { 5 }.

To find the data regularity using ontological primitives we consider

Domain space = { E i | i = 1, . . . , 100 }

described initially by 500 individual data pieces

{ < a(0), a(1), a(2), a(3), a(4) >k   | k = 1, . . . , 100  } .

We use the notation

< a(0), a(1), a(2), a(3), a(4) >k   | i    =   a(i) k

to be the i-th projection of the k-th framework, so

{  a(i) k  } = {  a(i) k   | k = 1, . . . , 100  }

is the set of values that have been placed into the i-th cell across the 100 events.

So the values for “event atoms” are {  a(i) k   }. 

The regularity of the data is then observed empirically when the size of {  a(i) k   } is < 100. 

Generalized n-grams, frames and scripts

The previous section indicates two things.  First, users might encode useful information directly into a gF Orb to produce a non-text analysis type knowledge management system.  We anticipate that gF Orbs will be used in the measurement and control of complex manufacturing processes.

Second, text analysis might be automated using multi-pass parsing that fills in a template based on various frames.

So full text Orbs might be replaced by gF Orbs when the gF was built based on linguistic type and linguistic rules.  It is our understanding that the Knowledge Foundation Mark 3 (developed by Richard Ballard) system envisions a gF type system that is not based on structure in natural language but which goes directly at the underlying information space that shapes natural language. 


Figure 7:  Parts of Speech and Parts of Discourse Framework

In either case, the contents of a frame can then be converted into a set

{  < a, r, b >  }

and then into a graph.  For example, if the order of the cells is not important one can treat one as a leading node and encode the rest as the nodes of a branch (as in Figure 8).  The information derived from a framework maybe encoded into our experimental system using the architecture in Figure 8.


Figure 8: Architecture for the Distributed Virtual Referential base

A couple of things can be said about the architecture in Figure 8.  The hash table has become a central tool in the development of very agile encoding of data in a “structure free” form.  In fact, the principle is that the encoding is random and occurs through the use of a hash function that makes a consistent but nevertheless random placement of information based on string values.  (There is a lot to talk about here.)  The placement of string values into a “structure free” form can be accompanied by metadata that is placed into what is called a hash table bucket.  One can put additional information about the string value into that bucket. 

In fact, using the class constructor notion, one can allow more than one object to be placed into a variable length hash table bucket.  Because of the modern object oriented hash table, one is able to perform localization of information in an efficient manner.  Localization of information may be derived from very large data sources and produce very small subject indicators.  These subject indicators can then be applied to entirely different data sources. 

Informational convolution

Information convolution is then defined to be a process that visits each element in a hash table and performs some logic using a small rule engine and the contents of the hashed element and associated bucket.

The key to making the Ontology Reference Base (Orb) operational is to have a simple encoding mechanism to encode informational bits.  The bits are required to have the form (class, object) where the class gets its definition from what is a stochastically defined neighborhood “around” all of the occurrences of the object, and the object gets its definition from a specific occurrence of a neighborhood.  Several reasonable methods may be used to define and refine class definition.  Initially, if one is using parts of speech tagging, the class is the part of speech perhaps with some additional information as contextual annotation. 

Using word level n-grams, as a start, one can define the center of a word’s neighborhood is a specific instance of the occurrence of a single word, or perhaps phrase or passage.  The value of this occurrence is used to generate the hash table key.  The Berkeley Data Base allows one to define a “memo” field as a hash table “bucket”.  The memo field allows one to store a long string and thus to store instances of neighborhoods for all occurrences of a word.   From this information one is able to develop a simple profile of occurrence and frequency, perhaps weighted by some control module.

The stochastically defined neighborhood “around” all of the occurrences of the object’s center is then developed using the information that is encoded into the memo field. 

The pair (neighborhood, object) is the same as (class, object) since the "class" is defined by the object's neighborhood.  The class is ideally a representation of ALL potential meanings of the chosen word. 

Two quite different processes are built on top of the hash table encoding of (object, local object neighborhood).  Both of these are designed to produce a human reification of semantic neighborhoods, from what is initially a structural analysis of the co-occurrence of words. 

The first process is called the voting procedure (Prueitt, 1997) as applied to a set of descriptively enumerated words or phrases.  This process will be explained a bit better later. 

The second process involves the development of new graph constructions from old ones using the notion of a convolution. 

Why does this give us high-resolution memetic detection informed by human tacit knowledge?  To answer this question, we turn to the neuro-psychology of memory, awareness, anticipation and to stratification theory (Prueitt, 2005). 

The most general model of a mental event is a single node with the set of structural linkages that are potential, but not necessarily actual.  So in the same way, one of the words (or phrases or passages – depending on that one wants to do) is the “center” of a model of linguistic variation.  The words occurring in the proximity of this center word are then treated as a potential indicator of the presence of linguistic variation used in social context to convey a meme. 

So, given this useful model of a mental event, how does a mental event develop?  How is “it” supported while it exists?  What are the consequences of a mental event existing?   The answers to these questions are given in reverse order.  The “future” consequences of a mental event existing are found in the formation of categories of sensory and cognitive invariances such as shapes, colors and textures. 

The support of a mental event is through coherence in electromagnetic resonance that draws on structure and energy in the neuro-pile (the substances of the brain).  The mental event develops under the control of anticipatory mechanisms within the human brain-mind system.  We use this parallel between Orb construction and the formation of mental events in the human mind.  This parallelism sets up very fast, microsecond processing, of informational convolutions using Fourier and integral kernel mathematics.  The result is a complete restructuring of the informational convolutions can occur, as it does in the human mind. 

Simple and Differential Convolution

Given that there is a traversal of graphs, effectively there are two possibilities at a node, (1) the traversal requires the production of a categorical container for occurrences of a string (object or class, or object), and (2) the traversal process does not require this production.

The adjectives “simple” and “differential” refer to the nature of the local rule engine.  The simple convolution is defined to be a process where by the rule for collapsing a category is based only on exact string matches.   The differential convolution is defined to be a process where by the rule engine has linguistic and ontology services.

The adjectives “partial” and “complete” refer to the global traversal.  The partial convolution applied the rule engine to some but not all of the nodes of the graphs traversed.  The complete convolution apples the rule engine to all of the nodes of the graphs traversed.

A graph may not be a tree and may not have orientations to the connections.  For example, the graph in Figure 9.


Figure 9: A graph with no orientation


However, the graph has a topology and the paths formed by nodes and connections can be traversed based on notions of nearness and similarity.


Figure 10: Topological neighborhoods for graph structures

A model may be used to specify the local convolution instructions, and to specify which graph structures are to be traversed and how.  In very simple cases, the situation involves only a gathering together of all occurrences of the same string in cases where the string is the label for one of the leaves in a set of simple trees. Very fast computer processes are available even in irregular cases.

In differential convolution, a series of local convolutions occur at nodes during traversals as each member of a set of local convolution instructions is processed.  So we might have an instruction that uses first order logic to determine if the collapsing of all occurrence of some string might be filtered so that some occurrences of the term are not treated in the same way. 

Global convolution instructions involve an instruction to apply a rule, or set of rules, to each node.  As a practical matter, this stratified application involves the two classes of convolutions, local and global. 

Localization and Organization Processes

Words may be annotated by parts of speech, or parts of ontology, tagging so that

{ w(k) } à  { (class:w(k)) }

At this point we have a set of (class:object) pairs.  An example would be (noun:”lake” ) with the class being “noun” and the object being the noun “lake”.  These pairs are then the labels of the branches in I. These branches are then the atoms that are organized into simple trees. 

A cross level organizational process is defined with the set of atomic units as the transform’s domain and a set of compounds as the transform’s range.  These organizational processes involve one or more convolutions and the application of convolution instructions. 

Convolution( A ) = Output set of graphs = O

We note here that A could be the Input bag, I, of 3-tuples (branches of length 3)

( (class:w(i)), (class:w(j)), (class:w(k)) )

where class ranges over either parts of speech or parts of ontology. 

Figure 11: Linkage between two mental events

In Figure 11, we indicate a picture of semantic valence between to localized bits of information. 


Figure 12: Differential linkages 

In Figure 12, we indicate that localized informational bits may have different types of semantic valiance.



Figure 13: Process of orientation and linkage formation in formative ontology

In Figure 13, we indicate the altering of local information bit orientation as part of a formative process that produces a graph structure.

The current experimental Orb is soon to be used to demonstration how the localization can be efficiently encoded, and how organizational processes are efficiently computed.

The capture of structure

American logician C. S. Peirce developed what is now called the Peircean “Unified Logical Vision” (Peirce et all, 1991),

“Concepts are like chemical compounds, they are composed of atoms.”

Figure 14: Diagram (Prueitt) on the Unifying Logical Vision

In chemistry, different compounds define a non-empty intersection of atom classes found within compounds.  So the exclusion of words from contention based on the word, or pattern, having been previously used is not consistent with principles we find on the scientific literature.  Overlapping compound chemistries are to be sought. 

We can see that local linguistic variation is modeled as if arrangements of chemical atoms.  In biochemistry, this physical arrangement is due to the complex conformational processes, such as found in protein folding.  This is “gene expression”.  In modeling the linguistic variation in text we are looking for “memetic expression” and have built a parallel between Orb computation and the natural science about human mental event formation.  In any complex manufacturing process we can build an analogous parallel between Orb computations of the physics involved in the manufacturing process.  In biological system, the folding process is the consequent to metabolic entailments. 

An organizational process is essential to modeling the metabolic reactions.  A similar dependency on organizational consequences is needed for machine inference about linguistic based on stratified architectures.  Again, we point to the facilitation of mutual-induction and the capabilities enabled by computer based differential and formative ontology using Orb constructions. 

Cross scale transforms are defined within discrete mathematics and have range and domain within different levels of organization.  The organizational cross scale transforms are formative and aggregative with the range of the transform a set of compounds.  The domain of the transform is a set of atoms.  The organizational transforms correspond to “dissipative processes” in physical systems.  The measurement transforms are in a dual relationship to the organizational transforms, in that there is often a commentator that acts as an inverse.  The physical correlate to measurement is an escapement processes.

The measurement cross scale transform localizes what is originally distributed information into atoms.  This localization can be via differential ontology framework and involve latent semantic indexing or neural networks. 

Cross Scale Transforms

The convolution operator

Convolution( A ) = Output set of graphs = O

suggests the form of the local to global cross scale transform. 

The domains for the elements (transforms) of a class of local to global cross scale transforms, G, is a set of atoms A, each localized into a (class:object) pair.   O is a set of graphs having the atoms of A as elements of the set of nodes related to the graphs. 

The range of any element of the transform G is a set (or bag) of compounds, C, organized by the effects of the transform G.

One can treat the class of local to global cross scale transforms as a category and then treat the category as a single object.

The form is then,

G ( A ) = C

Where A and C are the categories of localized and organized constructions.

The G transform is cross scale from localization to globalization of information. 

The measurement process, M, can be considered to be the inverse to G if one can find a specific measurement process to commune (i.e. be the inverse) with any specific element of G.

M ( C ) = A

The use of categorical theory is to be respected, since an ambiguity can occur in the matching of specific elements within categories, as defined. 



Edelman, G, (1987) “Neural Darwinism”, Basic Books

Penrose, R. (1993) “Shadows of the Mind” Oxford University Press

Peirce, C. S. et all (1991)  Peirce on Signs: Writings on Semiotic”, University of North Carolina Press

Pribram, K. (1991) “Brain and Behavior” Lawrence Erlbaum Associates New York

Prigogine, I. (1996)  “End of Certainty”,  Simon & Schuster, New York

Prueitt, P. (2005) “Foundations of the Knowledge Sciences”:, published on line at

Schank, R  (1977) ”Scripts, Plans, Goals, and Understanding: An Inquiry into Human Knowledge Structures”  Lawrence Erlbaum Associates

[1] URL: “Is Computation Something New?:

[2] An example is the gene. 

[3] URL: Chapter 4 in "Foundations":

[4] URL: Anticipatory Technology, A Challenge Problem:

[5] URL:

[6] For a review of opinions about this see the works of Robert Rosen and Sir Roger Penrose.

[7] URL: Paul Thagard’s work:

[8] Without going into a lot of detail, I refer the reader to the work by Nobel Laurent Gerald Edelman on response degeneracy in function-structure dynamics. 

[9] In around 1998, Bjorn Gruenwald, a resident of Pennsylvania USA,  started to use the natural ordering of integers to map text stings to points in a Hilbert space. A patent related to this work was awarded in 2000. 

[10] URL: Gelhard and Prueitt, Structural holonomy:

[11] Prueitt, Foundations for Knowledge Science: on line book: 


[12] A design for such a sign system was in one of the several proposals that almost received funding form the intelligence communities in the late 1990s and early 2000s


[13] Several of the chapters in the “Foundations” addresses the contributions of the Soviet applied semiotics school.  Quasi axiomatic theory is discussed in Chapter Six and a voting procedure implementation of quasi axiomatic theory is given in the first appendix. 


[14] A complete citation of the five or six yearly conferences is not available to me at this time.  A partial citation is given. 

Albus, J, A. Meystel, D. Pospelov, & T. Reader (Eds). (1995) Architectures for Semiotic Modeling and Situational Analysis in Large Complex Systems. 10th IEEE International Symposium on Intelligent Control 1995. Cynwyd, PA, USA. AdRem Inc.

Citkin, Alex (1996). Historical overview of the development of Quasi Axiomatic Theory and Situational Language in Russia (1920 - 1997), presented at the QAT Teleconference, New Mexico State University and the Army Research Office, December 13, 1996.

Dubchak, I; Muchnik, I. (1995). Classification Scheme for Complex Systems: Prediction of Protein Structure Models, in J. Albus, A. Meystel, D. Pospelov, and T Reader, (Eds), Architectures for Semiotic Modeling and Situational Analysis in Large Complex Systems, AdRem, Bala Cynwyd, PA

Burch, Robert (1996). Introduction to modern Peircean Logic with applications to automated reasoning, presented at the QAT Teleconference, New Mexico State University and the Army Research Office, December 13, 1996.

Finn, Victor (1996a). Plausible Reasoning of JSM-type for Open Domains. In the proceedings of the Workshop on Control Mechanisms for Complex Systems: Issues of Measurement and Semiotic Analysis: 8-12 Dec. 1996

Finn, Victor (1991). Plausible Inferences and Reliable Reasoning. Journal of Soviet Mathematics, Plenum Publ. Cor. Vol. 56, N1 pp. 2201-2248

Lefebvre, V. A. (1996). Reflexive Control and Intelligent Agents. In the proceedings of the Workshop on Control Mechanisms for Complex Systems: Issues of Measurement and Semiotic Analysis: 8-12 Dec. 1996.

Michalski, R. S. (1994). A Theory and Methodology of Inductive Learning, in R. S. Michalski, J. G. Carbonell & T. M. Mitchell (eds), Machine Learning: An Artificial Intelligence Approach, Morgan Kaufmann, Los Altos, CA.

Mikheyenkova, Maria A. (1995) Application of JSM-reasoning to problems of sociology, in J. Albus, A. Meystel, D. Pospelov, and T Reader, (Eds), Architectures for Semiotic Modeling and Situational Analysis in Large Complex Systems, AdRem, Bala Cynwyd, PA.

Pospelov, Dmitri (1996b. Basic concepts of Situational Languages and formal means of analysis and control of natural systems , presented at the QAT Teleconference, New Mexico State University and the Army Research Office, December 13, 1996.

Prueitt, Paul S. (1996c). Structural Activity Relationship analysis with application to Artificial Life Systems, presented at the QAT Teleconference, New Mexico State University and the Army Research Office, December 13, 1996.

Rocha, L. M. (1996). Evidence Sets: Contextual Categories, in the proceedings of the Workshop on Control Mechanisms for Complex Systems: Issues of Measurement and Semiotic Analysis: 8-12 Dec. 1996.

Tzvetkova, Galia (1995). A general view on complex control systems: their evolutionary development and intelligence. In J. Albus, A. Meystel, D. Pospelov, and T Reader, (Eds), Architectures for Semiotic Modeling and Situational Analysis in Large Complex Systems, AdRem, Bala Cynwyd, PA

Zabezhailo M. I (1996). The Application of QAT reasoning to Forecasting the Delayed Effects of Environmental Degradation on Human Health, presented at the QAT Teleconference, New Mexico State University and the Army Research Office, December 13, 1996

Zabezhailo M. I., Finn V. K., Blinova V. G., Fabrikantova E. F., Ivashko V. G., Leibov A. E., Melnikov N. I., Pankratova E. S. (1995) Reasoning Models for Decision Making: Applications of the JSM-method in Intelligent Control Systems, in J. Albus, A. Meystel, D. Pospelov, and T Reader, (Eds), Architectures for Semiotic Modeling and Situational Analysis in Large Complex Systems, AdRem, Bala Cynwyd, PA