OntologyStream Inc Briefing


Elementary Tutorial on categoricalAbstraction (cA)


August 2, 2002







Behavioral Computational Neuroscience Group (BCNGroup) provides independent feasibility studies of knowledge system integration processes.  The Group has a ten-year history. 


In 2001 and 2002, the general concept of a Knowledge Operating System (KOS) was proposed and in this context we describe how human-community communication characteristics might be transformed into semi-structured economics based on knowledge sharing. 


The BCNGroup believes that research on the deployment of KOS systems is evolving into applied knowledge science.  Tools are being developed to fit specific community needs.  The KOS development environment is currently available under a site license at $19,500. 


Training in KOS design and standards is available from The OntologyStream.  BCNGroup individual membership, and corporate sponsorship program information, is available from the web page, www.bcngroup.org. 


This tutorial is on what some regard as a deconstruction of the mathematics and technology of text and data indexing.  The result is deemed a type of Synthetic Perception about the invariance in data and the development of human annotation of what humans regard as meaningful.  Synthetic Perception is seen as a by-pass of current data-mining and text-indexing methods




Copyright 2002, The OntologyStream Inc






Philosophical Overview:  Our Knowledge Management (KM) problems stem from past KM methodologies.  Currently, communities attempt to improve knowledge sharing practices by contracting for new computer technologies. 


In the first step of a knowledge technology deployment one objectively evaluates proposed technology and methodology and develops an understanding of what is available in the marketplace.  One must know what is available in computer systems and from innovations in various supporting communities.


A bottom line is that the human experience of knowledge be shared.  At core this is the nature of human communication.  A disinterested third party cannot have a vested economic interest, particularly one that is controlling of all other interests.  The community at large loses.  Society loses. 


Only in an economically unencumbered environment can one expect that concept base indexing and the propagation of knowledge be accomplished.  The compensation for knowledge sharing has to be accrued to the individuals who are sharing this knowledge. 


The tutorial will provide a full disclosure of a fundamental discovery of categorical abstraction and the inventions of stratified theory in the context of knowledge technologies. 


Due to the 2001 War on Terrorism, the government is prepared to scale up IT support for homeland security.  The problem is in the capture and management of meaning and the inability to extract meaning using purely computational means.  In a knowledge war, our conventional IT 'weapons' are weak.  In theory, they could be much stronger.


One must look to natural science and shift from word-based indexing to concept-based indexing.  Natural scientists surmise that a concept can be identified and processed directly, and with revolutionary effects.  But it is not a simple matter to bring this principle into full application. 


The situation is analogous to World War II.  Scientists surmised that munitions are much stronger if they were based on a completely different principle -- a nuclear reaction rather than a chemical reaction.  The Manhattan Project acted on that theory.  Later peaceful uses of nuclear power where developed. 


We propose a new Manhattan Project for Knowledge Technology (KT) that will give the Nation a decisive tool in the knowledge war.  As the War is won, we expect to see human productivity increase while the National leads the World in addressing the root causes of this unfortunate war.


What we propose is a project that allows leading scientists to concentrate on the problem and allows engineers to bring the solution to fruition.  It requires stripping away some of the institutional impediments that have been retarding this development.


Initial Work Outline:  Any “conceptual space” associated a knowledge system can be mapped following these steps.


1)      The map is produced by collecting together between 100 and 200 samples of the description of technologies, theories and frameworks (using web searches and in house materials). 


2)      Once this sample is available as a text collection, we write a simple parser to produce a categorical abstraction input file (datawh.txt) that is discussed in the tutorial.


3)      The OSI Knowledge Operating System (OSI KOS) is used to record human perceptions about the structure in this input file and render topic maps (XML) for inspection and comment.


The mapping process, of course, has various levels of resolution. OntologyStream Inc develops a broad and definitive model of the IP (Intellectual Property) and conceptual space that surrounds” the basic sub concepts of all knowledge system technology.  This work is preparatory for


1)      The full mapping of all conceptual themes related to the knowledge system’s subconcepts in both the US PTO database and in the Internet public literature.


2)      The production of dedicated patents covering the work of those developing the deployment plan and observing the progress in the deployment.


3)      Informed decisions over technology acquisition during integration.


The BCNGroup Charter defines a science-based Intellectual Property management structure that serves the community of innovators supporting the knowledge technologies.


This management structure is designed to serve business partners as well as innovation processes, and is the basis for coordinated development of knowledge technology and knowledge science.   


System description



Knowledge Operating System (KOS) can be used to track global trends and anticipate events. The system brings together a variety of innovative components to provide an "intelligence-vetting engine" that globally tracks emerging events related to any topic or event type.  The necessary condition for seeing the event is that a sensor must produce data structure indicative of the event.  Categorical Abstraction bypasses the complexity issue in massive data sources by replacing massive data with a very much smaller set of categories.  The categories can be used to retrieve all of the data that will produce individual categories, so we have a true "compression" of data into information... and the compression may be as much as a million to one. Novelty detection falls out of this process since a single occurrence of a data element will appear as a new category if such a data element is in fact novel. Event chemistry opens this cA substructure into a biologically feasible information routing and retrieval architecture based on the Prueitt tri-level architecture { memory, awareness, anticipation }.  Machine inference and situational simulation as well as sense making is enabled



Collection – KOS will automatically monitor information flow in the Internet on a 24/7 basis, looking for new items that are related to the subject and events of interest.  KOS software agents look for new and novel relationships not previously anticipated and send data structures into centralized information vetting areas staffed by humans. 


For example, all Internet published scientific conferences in a specific area of interest might be mined to produce trend analysis of intellectual property.  Concept mining in KOS is language-independent.



Annotation - Human annotation of trends can be done in one’s native language and incorporated into a single, multi-language knowledge base.  (By avoiding translation of any inputs, meaning is preserved and the significant costs and delays of translation are avoided.) Topic maps in any language are constructed using the OASIS standard. 


Storage - Our collected information is stored in formats that allow an object to be directly related (“structurally coupled”) to any other object.  The relating structures are independent second order control mechanisms that support query, routing, and anticipatory responses. 


A tri-level architecture is used that separates: (1) known events, (2) categorical abstractions (cA), and (3) aggregations of categorical abstractions (event chemistry or eC) under the constraints of a knowledge base.


Extraction - A number of mature technologies extract information from data sources. This information is diffused into a substructure layer (cA) of information that serves the agile reconstruction of information in context (eC).  The agile technology allows us to look at an object of investigation from many different perspectives.  


The extraction process is represented as categorical invariance in the patterns of word expressions and processed into a central, sparse knowledge base.  Information compression, routing and inference processes are achieved using a technique (I-RIB) that renders visually as graph structures expressing structural relationship and in auditory form.


Interaction with analysts - A number of analytical tools automatically develop ontologies and taxonomies.  KOS logical and structural relationships are rendered visually or optionally with sounds.  The overall structure of a given area of knowledge is rendered visually.   Various scenarios are generated and humans are assisted in exploring variations in strategies and in storing work product related to these investigations.  The system itself can be used to analyze analyst performance. 


Simulation and sense making – In KOS, the cognitive load is allocated to the human.  The conventional approach, of formal deduction or computational expert systems, is replaced with an extension of quasi-axiomatic theory coupled with human experience within the KOS visual and auditory environment and within the community of KOS analysts.


What-if scenarios and conjectures about causes take a new form where humans in small communities develop meaning in dialog about KOS-defined event structures.


Display – KOS provides breakthrough capabilities for identifying and monitoring early indicators of significant change.  Visualization of the categories of data and relationship among these data enhance the ability of analysts to anticipate emerging events.



The remainder of this briefing will provide a precise discussion of our methodology, including the OSI categoricalAbstraction (cA) engine and event Chemistry (eC) engines.  We start with a download of software at




which is 298K in a WinZip file and 1 Meg when unzipped. 



Figure 1: The unzipped file for this tutorial


The tutorial Data folder starts only with a small file called datawh.txt containing the following text:


IPaddress         eventType

109                  E1

110                  E1

101                  E2

101                  E3

109                  E4

105                  E3

105                  E2

106                  E3

107                  E3

102                  E5

103                  E6

104                  E5

108                  E1

109                                    E3


We will not use the Splitter.exe in this tutorial. 



Figure 2:  The SLIP conjecture with atoms = IPaddress


Open SLIPWH.exe and type in “a = 0” and then “b = 1” in the command line to produce the link conjecture seen in Figure 2.  There are spaces around the “=” sign in these commands.  Type “Help” to see the list of knowledge operating system (KOS) verbs available from here.  Call 703-981-2676 to ask a question.


Now issue the KOS commands “pull” and “export”.  Again, the command “Help” will give more information about the KOS commands.


Close the SLIPWH.exe and look into the Data folder.  You will find:



You should open each one and see if you understand how each was created and what each of these data structures may be used for.


Links.txt contains


101                           E2           E3

102                           E5

103                           E6

104                           E5

105                           E2           E3

106                           E3

107                           E3

108                           E1

109                           E1           E3        E4

110                           E1


The first line in Links.txt indicates that the address 101 has been associated with E2 and E3 by the SLIP conjecture. 


It is important to note that two things have happened up to this point.  First some process created the original datawh.txt.  The second thing that has happened is that the SLIP conjecture is used as a conjectural convolution over this datawh.txt file.  There are many ways to create the datawh.txt files and many ways to create conjectural convolutions.  But we are taking a simple example.  The process that produces the datawh.txt file is completely up to the user of the OSI browsers.  However, at this point the OSI software  only offers the simplest of the convolutions based on simple link analysis. 


Paired.txt contains:


















These are pairs of elements from the column that was selected to produce atoms.  The nine unique elements that are either first or second position in these pairs is the set:


{  101, 102, 104, 105, 106, 106, 108, 109, 110 }


103 is not in this list because E6 occurs only once in the eventType column and so there is never a fulfillment of the SLIP conjecture that involves 103.  The generalization to the class of convolution operators might be anticipated by how the SLIP conjecture produces atoms based on finding all instances where the conjecture holds true. 

One way to generalize this is to use Frank Schank type frames with slots and fillers.  Atoms are then things that are found to occupy slots. 


Now open the browser SLIPCore.exe and issue the KOS commands “import” and “extract” to produce the screen in Figure 3a.  Click once (not twice) on the A1 node to produce the scattering of the atoms.




a                                                      b


Figure 3.  The Core Browser (a) before clicking on the A1 node and (b) after


The nine atoms in the set of “all” atoms is scattered onto the surface of a two dimensional sphere.  (This is generalized to allow “dimensions of information processing” to n dimensional spheres.) 


The clustering on the sphere is similar to a Kohonen feature extraction algorithm (artificial neural network) but is simpler and may be more powerful.  The clustering algorithm is a form of scatter-gather techniques that have been used in the text understanding research field for perhaps two decades.  However, the way that the scatter-gather is done is unique to Prueitt’s work and is simpler and more powerful. 


The technique itself has one additional innovation based on the conversion of the ASCII into a line in number base 64.  This conversion allows one to very quickly answer a set membership question.  This question is about whether or not a pair randomly selected from the set of all possible pairs of atoms is in the set of pairs in Pairs.txt.   There are 9 atoms in this case, so there are a possible 81 pairs that can be produced. 


The Pairs.txt file has 15 members.  In this case the set membership problem is easy.  A random pair has a probability of 15/81 of being in the Pair.txt file.


However we have data sets that contain 10,000 members. In this data the set of possible pairs is greater than 10,000,000.  In this data set the atoms are ASCII stings that have between 10 and 40 characters.  This means that the membership question requires that a string match be made between a text string of between 20 and 80 characters and a string of ASCII that is 10,000*80 = 800,000 characters long. 


The critical computational requirement is this membership question, and database solutions are far to slow.  We need to resolve 10 million membership questions to complete the average scatter gather task. 


This membership question can be addressed in many ways, but perhaps the most optimal way is to pad out each of the 10,000 members to have a length equal to the maximum length over the entire set, say 80 characters and map this to memory. 


One needs less than one Meg of memory to accomplish this task.  Then the set membership question can be answered in less than 20 fetches (the contents of one of the 80 character data “cell”), compare (the contents of the cell to the pair that one is asking the membership question of.) steps!  Why?   (The answer is not proprietary; it is just best to figure this out for oneself.  Hint: 2^20 > 800,000) 


The scatter-gather requires that this single membership question be asked and answered perhaps 10,000,000 times.  This required about four hours in FoxPro in our early studies.  However, when we used the In-Memory map we find that this take less than 30 seconds. 


It has been a few months since Prueitt saw this resolution of the membership question, and he has developed a few other approaches to this, but each of these other approaches are slower than the algorithm suggested above.



Figure 4: Creating subcategories


Moving on to the clustered data.


By clustering the data in the tutorial set we find that there are three clusters.  Type in “random” in the command line of the Core Browser, and then type in “cluster” to see the clusters form.  The three clusters can be moved into subgroups by using a command


“a, b -> categoryName”


as done is Figure 4. 


See the text in the Command Line in Figure 4, and perhaps type Help into the command line.


The clustering process in the scatter gather is fast and finds a unique decomposition of the elements from the bag of atoms into a set of categorical primitives, such as seen in the next figure where the size of the set of atoms is 2395. 



Figure 5: From http://www.ontologystream.com/cA/papers/EventDetection.htm


However, in our case we have only three categorical primitives (called stratified primes).



Figure 6: We have 6 simple compounds each developed by a single link and 9 atoms


These three primes are composed of five simple compounds (each defined by one link) and the nine atoms.  On can see this by double clicking on the A1 node to produce the screen in Figure 6 (the KOS browsers have four re-sizable windows and you can readjust your sizes. 


Then close the browser and the software remember the previous settings.) 








Figure 7: The five simple compounds


Now we can alter the datawh.txt file so that one gains a better intuition about what is possible with cA and eventChemistry. 


Close all of the KOS browsers. And put the folder (Figure 1) on the desktop.  Make a copy and name it what ever you wish.  Having both on the desktop and no programs running is helpful.  Now go into the Data fold of the copy and delete all of the files and the folders in the data folder except the datawh.txt file.  Open this file up and add a new line:


105                                       E4


Be sure to put one tab between “105” and “E4”. Now repeat the steps to produce a set of atoms.  You will get the new categorical Abstraction seen in Figure 8:



Figure 8: The categorization with the new data element added to datawh.txt


The new compounds are given in Figure 9.







Figure 9: The updated compounds


Second Change to datawh.txt


Now make a third copy of the folder and delete all of the data except of the datawh.txt file again.  Take all but the first line and copy in several times into the same file (not introducing blank lines.)  Now redevelop the cA and eventChemistry.  You will find that the Core Browser will have the exact same data. 



Figure 10:  The cA and eventChemistry after adding duplicate data


This is a property of the fact that all categories are already present before the additional data is added.  The additional data is not introducing any new categories.  One can compare Figure 10 to Figure 6 and see that everything is the same.


Root_KOS (root Knowledge Operating Systems) Overview


Root_KOS loads and saves tabular files to/from memory, and responds to scripted commands.


Loading and saving tabular files is important because SLIP Browsers work with data that is in a system file or in a special In-Memory Referential Information Base (I-RIB) data structure.  The SLIP Warehouse and SLIP Technology Browsers transform data that resides on text files. (See Figure 1).  Both depend on a Root_KOS kernel. 



Figure 11: KOS Browsers work together


The Warehouse Browser takes any tab delineated audit log and quickly produces a data mart and a combinatoric expression of link analysis within the values of an event log.  Both of these files are produced using In-Memory Referential Information Base techniques.  Once the files are produced then the Technology Browser can use them. 


The Technology Browser uses In-Memory RIB techniques to develop event detection. The Event Browser (currently underdevelopment) is launched from the Technology Browser and some data resources are exchanged.  SLIP atoms are identified in the Technology Browser and those atoms involved in an event are conveyed to the Event Browser.


The I-RIB uses system files, memory maps and mathematical objects such as lines and arrays.  OSI’s I-RIB technology is derivative of mathematical formalism called structural holonomy. 


Figure 12: Some early event chemistry drawings


Structural holonomy is the innovation of Paul Prueitt and is based on his interpretation of the work of renowned neuroscientist Karl Pribram.  This formalism is of the nature of mathematics and yet has grounding in experimental literatures from biology and neuroscience.  The basic work has been privately peer reviewed from over a decade.



Figure 13:  One of the early event compounds


The underlying concepts of structural holonomy is being made public domain in order to facilitate the development of I-RIB systems in support of knowledge technologies that depend on very fast data aggregation methods.



Figure 14: The Root_KOS User Interface and data structures



OSI’s I-RIB technology is a full data base management system that is designed to minimally cover the requirements of many classes of data aggregation, artificial neural network, evolutionary programming and data warehousing systems.  The smallest version of the I-RIB technology is part of the 172K SLIP Warehouse and the 348K SLIP Technology Browser.  Both of these systems are operational.


The Root_KOS is marketing as a development environment, complete with a minimal I-RIB system.  Yearly site license is $19,500 for the development environment.  Root_KOS is applicable to elementary research in Natural Language Processing, full text mining and warehouses, and certain types of eBusiness functions.  The development of deployable applications are streamlined.


Any KOS Browser can recognize scripted commands by (1) command line input (2) certain mouse events on nodes of arcs in the graph window, or (3) mouse events on the node tabs at the top of the graph window. The exit and help functions are the most basic of all scripted commands.


Scripting provides for user gestures as response to the presentation of state information from an internal ontology or finite state machine.  Algorithmic responses to a human gesture produce changes in


1)      The ontology or finite state machine,

2)      Changes in auxiliary resources such as system files and

3)      A textual response in the response line and/or a sound response.


KOS Browsers have:


A.1:  Modal transforms that switch the view in display areas and change the system’s response to script commands

A.2:  Graphs that are generated from a process model.  The elements of the graph are active objects.

A.3:  Allow the selection and movement of objects within the graph.

A.4:  Selection and movement will change the state of corresponding ontologies or finite state machines.

A.5:  Selected objects will refer to contents.  So for example, selecting a node and typing “Open Event Browser” (or “oeb”) will take the contents of the node and move this content to a new instance of the Event Browser.  Selecting a node and typing cluster” (or “c”) will cluster the atoms corresponding to that node.

A.6:  Grammatical interface composed of a command/response line with history.


KOS Browsers have a formal Program Interface (PI) that is completely implemented through a categorized message stream interface.  The machinery for the PI is complete in the Root_KOS and extendable in any KOS Browser. 


Project plumbing in the root KOS provides maximal notational affordance by using extensible graph based formalism. 


Notation on states and gestures extend the KOS foundational notion:  The notation for states, gestures and locations is:


The set of world states S = { sj }.

The set of gestures G = { gi }.

The set of locations L = { Lk }.


A formal theory of states and gestures provide a computational means to discuss event paths in human computer interactions, particularly for telelearning, distance learning, and virtual knowledge collaboration. These states can be used as part of the mechanics of what we call a "knowledge processor".


The notion of location allows for the development of enterprise KOS. 


The formal theory of states and gestures is built from a precise formalization of computer game and user interactions in Multiple User Domains (MUDs) (such as the Palace 2-D chat environment) and Role-Playing Games (RPG) (such as ChronoTrigger or Zelda.) 


Gestures and states can be modeled as the fundamental units of a specific finite state machine. Thus, under any such designation, the related model of event sequences is computable.  The KOS, however, must represent the invariance in the data AND the mental states of humans.  This means that our effort to representation the contents of mental events within the context of discourse, should be split into two parts. These two parts are


1)            The aggregation of data invariance and

2)            The representation of user response history in terms of the set of aggregated invariance.


The aggregation of invariance is used to represent the computer processes, and the user response history is used to represent the natural world.  The communication between finite state machines is used to control and allow user (community) focus on a specific set of issues.  This control of focus provides universal “Informational Transparency with Selective Attention”. 


We can assume that a set of states, S = { sj }, are created before hand and the gestures G = { gi } are a set of stored responses. This would mean that S and G are actually the atoms of finite state machine. However, the existence of event states may be actually implicit unless actually instantiated as part of an event. In this case, it is proper to refer to S and G as virtual finite state machines.  In the course of working with the KOS Browsers, users select gestures in response to a presented state from the computer. This pairing of state and gesture is a represented as a mutual decision event.


In the Event Chemistry being developed by OSI, the finite state machine is a virtual combinatoric expression of the aggregation of abstractions called “SLIP atoms”.  This abstraction plays a role similar to the abstractions we have in physical chemistry.  Each atom has a specific set of linkage potential.  The manipulation of the linkage potential (called “valence: in physical chemistry) leads to the formation of chemical compounds. 


The notions of an “atom” and “chemical valence” are useful abstractions.  In the Event Browser we use a different set of abstractions to visualize the parts of events and the means that these parts have to be a compound in a larger event. 



Figure 15: event chemistry


An abstraction from the signatures of real occurrences leads to event chemistry.  We have developed an additional capability. This capacity is to provide a unique situational analysis based on the relationship of part to whole as revealed in the formal literature of Russian applied semiotics and related literature in the West.


Definition: The term formal system refers to a four-term expression:


M = < T, P, A, R>


where T = set of basic elements, P = syntactic rules, A = set of axioms, and R = semantic rules.  The interested reader can refer to Situational Control for a more detailed treatment of formal systems.


For our purposes we need only refer to a figure from page 37.



Figure 16: Taken from Pospelov Situational Control


In figure 16, the set of base elements T are combined in various ways to produce three types of sets, axioms, semantically correct aggregates, and syntactically correct aggregates. We should remember that mathematical logic is founded on a similar construction and therefore that most of the results of mathematical logic will somehow apply later on to the theory of knowledge processing that we are constructing. For example, the set of axioms can be specified to consist of independent, non contradictory and self evident statements about the set of base elements T.


The axioms are our analog to the quantum mechanical substrate that gives rise to the mechanisms that in turn produce some of the material and energetic constraints that are involved in the creation of awareness. Rules of inference can also be formulated to maintain notions about true or false inference from assignments of a measure of truth to the axioms.


The set of syntactically correct aggregations of elements of base elements can be defined either by listing or by some implicit set of rules.


The semantically correct aggregations could then be interpreted as those syntactically correct aggregations that have an assignment of true as a consequence of the inference rules.