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Differential Ontology Framework


Appendix to :  Knowledge Technologies and the Asymetric Treat


Paul S. Prueitt, PhD



Computers are not now, and likely will never be cognitive in the same way as humans are.  However, the notion that cognitive-like processes might be developed has brought some interesting results.  At the core of the solutions that are been, or are likely to soon be, made available is a class of the machine-encoded dictionaries, taxonomies and what are often called ontologies.  While encoded dictionaries, taxonomies and ontologies are often referred to as knowledge representation, one has to be careful to point out that knowledge is “experienced” and that these computer data structures are experienced only when observed by a human.  Some experts in the field express the notion that computers do or will experience, and this is the so-called strong AI position. 


The rejection of strong AI opens up an understanding that knowledge definition, experience and propagation requires a greater degree of agility and understanding by users of the processes that have been developed by the strong AI community over the past 50 years.  There has been a failure to communicate.


The strong AI community, on the other hand, should eventually come to support the principled arguments made in the quantum neuroscience community.  Quantum neuroscience has an extensive literature that reports on issues related to human memory, awareness and anticipation.  This literature is referenced in separate technology volumes, simply because the purpose of this paper is to develop concepts not to provide what should be a complete citation of the literature (as opposed to a very partial citation that might be misleading.)  However, we point out that the quantum neuroscience literature addresses the question of how things happen and in doing so this literature challenges classical Newtonian physics as a model of natural complexity.


The cause of events has a demand and a supply component.  Demand-side knowledge process management can be used to create machine-encoded ontologies.  These formal constructs, that are the states of computer programs, are constructions that exist in two forms, implicit and explicit.  Implicit constructs are defined as proper continuum mathematics.  The constructs of continuum mathematics are represented on the computer in a discrete form.  The discrete form of implicit ontology has the benefit of the precision of the embedded formal continuum mathematics, seen in mathematical topology, mathematical analysis.  Demand is a holonomic, e.g., a distributed, constraint like gravity and so a distributed representation is needed.  The continuum mathematics provides the distributed representation that the computer “cannot” provide by itself. 


An explicit ontology, on the other hand, is in the form of a dictionary or perhaps a graph structure.  The constructs of explicit ontology are expressed as discrete mathematics, graph theory, number theory, and predicate logics.  The interface between discrete mathematics and continuum mathematics has never been easy, so one should not expect that the relationship between implicit and explicit ontology be easy either.  However, a formal theory of by-pass has been developed, by Prueitt, which shows a relationship between number base conversions, data schema conversions, and quasi-axiomatic theory [1]. 


First-order predicate logics are often developed over the set of tokens in some of the explicit ontology that exists, for example by using a standard resource description framework (RDF).  Value is derived, and yet these ontologies with their logics suffer from the limitations of explicit enumeration and relational logics.  This limitation is expressed in the Gödel theorems on completeness and consistency in formal logics [2] as well as in other literatures.  By-pass theory is designed to manage this problem.


The bottom line is that high quality knowledge experience and propagation within communities needs the human to make certain types of judgments.  But the methodology for human interaction with these structures is largely missing, and is certainly not known by most of those who need now to use these structures for national intelligence vetting. 


We introduced the term “Differential Ontology” to talk about a human mediated process of acquiring implicit ontology from the analysis of data. 



Figure 1: Differential Ontology Framework


By the expression “Differential Ontology” we choose to mean the interchange of structural information between Implicit (machine-based) Ontology and Explicit (machine-based) Ontology.


         By Implicit Ontology we mean an attractor neural network system or one of the variations of latent semantic indexing.  These are continuum mathematics and have an infinite storage capability.

         By Explicit Ontology we mean an bag of ordered triples {  < a , r, b > }, where a and b are locations and r is a relational type, organized into a graph structure, and perhaps accompanied by first order predicate logic.


The differential ontology framework uses implicit ontologies now found in stochastic and latent semantic indexing “spaces” and derives a more structured form of dictionary type ontology.  The class of process transformations between implicit and explicit forms of machine ontology is to be found in various places.  For example, we have seen market anticipation in the large number of automated taxonomy products that are appearing in the marketplace.  However, we claim that the notion of deriving explicit ontology from implicit ontology is an original contribution. 


Within the explicit ontology there are localized topics.  These localized topic representations “sit’ by themselves. In the implicit ontology the information is distributed like gravitational wells are in physical space.  Move anything and everything changes; sometimes only minutely and sometimes catastrophically.  The perturbations of representation are then formally seen as an example of a deterministically chaotic system.  Natural systems may or may not be deterministic, and thus the argument is that formal chaos is not the same as the process seen in the emergence of natural systems in the setting of real physical systems.  Neural network type attractor manifolds is an early form of the implicit ontology.  But now we have also genetic algorithms, the generalization of genetic algorithms in the form of evolutionary programming and other mathematical constructs.  The tuning of these systems to the physical reality is thus of major consideration.   This tuning is not a done-once for-all-time task.  As the world changes, the tuning of implicit ontology must change also.  How is this to be done?


Moving between these implicit and explicit forms of machine ontology "state gesture mechanisms" can be attached to topic constructs, whether distributed or localized, using new type of “stratified” architecture [4-6] that is grounded in cognitive neuroscience, specifically in the experimental work on memory and selective attention [7,8].  The stratified architecture has multiple levels of organization, expressed as an implicit or explicit, continuum or finite, state machine, in which within each level certain rules and processes are defined. 


Cross level interaction often MUST involve non-algorithmic [9] movement within the state spaces.  Thus a human, who CAN perform non-algorithmic inference, is necessary if the over all differential ontology system is to stay in tune with the external complex world.  This means that implicit and explicit formalism is NOT sufficient without real time human involvement.  A state gesture mechanism drives the information around that part of the system that lives in the computer, but the demand for this supply comes from within private personal introspection, perception and decision-making by humans.  Again, our viewpoint seeks to return responsibility, for control actions in the world, to the human and push away the notion that the crisp and precise states within computer information systems can reasonably be managed outside of this responsibility. 


State gesture mechanisms allow the machine ontologies to be “assistant-to” human decision making.  The mechanism is not a closed formalism or an information technology, but rather an intellectual framework with stratified theory and cognitive neuroscience as the framework’s grounding [10]. 


Following architecture, and design of a related applied semiotics theory developed by Pospelov and his colleagues [11], the state gesture mechanism itself is deemed largely subjective.  This means that the mechanism is not reducible to algorithms.  A ‘second order’ cybernetic system is required that is primarily controlled by direct human intervention.  So the machine ontologies are required to be sub-servant to a human knowledge experience process.  The details of the machine ontologies are visible as reminders or signed informants within a sign system or natural language.  It is for this reason that one can call this a knowledge operating system.


Elements of micro-ontologies, that are formative within the moment, act as signs about the knowledge process that are regularly occurring in social networks.  The differential ontology framework requires a human interaction with these signs.  That is the Demand side.  Ontologies are streamed using formatted micro-ontologies from point to point in the knowledge ecosystem resident to the community of practice.  This is the Supply side. 


A computational mirror of the state gesture mechanism is also “assistant-to” the location where information is moved within the enterprise.  So the mechanism acts as an automated reporting and assessment technology.  This assistance has great value to social and economic processes.  Productivity goes up.  Social value goes up.  The fidelity of knowledge representation goes up.  Return on investment goes up. 


Responsibility can, and should, be assigned exactly where responsibility is situated.  This is true, in particular, where Constitutional rights to privacy are involved.  A knowledge operating system, such as the Knowledge Sharing Foundation, can provide complete transparence to all instances where a human examines private knowledge. 


As an example, an evocative question can be answered in various ways.  The answers made are part of a natural language generation capability that involves the emergence of word structure from a mental experience.  This emergence must involve a human awareness, and the action of requesting the computer supporting processes can be a trigger to reporting mechanisms about the inspection of private information.  This the barrier to inspection is transparent. 


The structure of differential ontology mediated communication allows a mechanical roll-up of the information into one of several technologies for natural language generation from semi-structured information.  However, the process is formally underdetermined, and some constraints must be imposed during the construction of the natural language response.   One sees the same situation as the mathematics of the wave functions in quantum mechanics.  The formal mechanism for “collapsing the wave” and realizing locality cannot be derived from the classical notions, and perhaps cannot be derived at all in a single formal system (having both completeness and consistency).  Many post-modern scholars of physics have equated this problem with the notion of finding a single unified theory of everything [14]. 


Differential micro-ontologies represent the first of a new generation of more complete (supply side plus demand side) knowledge process management paradigms.  Machine based ontologies generate natural language that communicates to users in a way that is familiar.  This drives knowledge sharing in a new way. 


What is surprising about this vision is that it is NOT the popular Artificial Intelligence vision of the future.  The “real” future brings the human more fully into contact with other humans within what is essentially a Many to Many (M2M) communication device.


Advanced notation for Formative Ontology and Differential Ontology





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


[2] Nagel, W and Newman, J. (1958). Godel’s Proof. New York University Press.


[3] Prueitt, P.S. (1995) A Theory of Process Compartments in Biological and Ecological Systems. In the Proceedings of IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large Complex Systems; August 27-29, Monterey, Ca, USA; Organizers: J. Albus, A. Meystel, D. Pospelov, T. Reader


[4] Edelman, G. M. (1987). Neural Darwinism. New York: Basic Books.


[5] 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.


[6] Prueitt, P. (1998). An Interpretation of the Logic of J. S. Mill, in IEEE Joint Conference on the Science and Technology of Intelligent Systems, Sept. 1998.


[7] Levine, D. & Prueitt, P.S. (1989.) Modeling Some Effects of Frontal Lobe Damage - Novelty and Preservation, Neural Networks, 2, 103-116.


[8] Levine D; Parks, R.; & Prueitt, P. S. (1993.) Methodological and Theoretical Issues in Neural Network Models of Frontal Cognitive Functions. International Journal of Neuroscience 72 209-233.


[9] Prueitt, P. (1997b). Grounding Applied Semiotics in Neuropsychology and Open Logic, in IEEE Systems Man and Cybernetics Oct. 1997.


[10] Penrose, Roger (1994). Shadows of the Mind, Oxford Press, London.


[11] Pospelov, D. (1986). Situational Control: Theory and Practice. Published in Russian by Nauka, Moscow.


[12] Park, S; Hunting, S; and Engelbart S; (Editors) (2002). XML Topic Maps: Creating and Using Topic Maps for the Web. Addison Wesley


[13]  Maturana and Varela; (1989) The Tree of Knowledge 


[14] Nadeau, R, Kafatos, M; (1999).  The Non-local Universe, the new physics and matters of the mind.  Oxford University Press.


[15] Albright, M; Kohut, A (2002). What the world thinks in 2002, The Pew Global Attitudes Project, The Pew Research Center for the People & the Press.


[16] Prueitt, Paul S.; (2002).  “Transformation of Knowledge Ecology to a Knowledge Economy”, KMPro Journal.