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Quantum Relation Technology - Theoretical Background

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The Quantum Relation Technology (QRT) uses an entirely new and revolutionary data representation and processing model based on the Quantum Relations Theory (more on Quantum Relation Theory). This model provides an innovative method of creating, storing, and processing extremely complex knowledge representations, based on techniques and methods derived from modern mathematics and quantum physics. The QRT model encapsulates data and software under single multi-dimensional structures called Data Fusion Objects (DFOs). The DFO model permits a hierarchy of discrete knowledge items, which interact within larger multi-dimensional structures called Frames of Reference (FORs). As a conceptual model, a DFO can be considered a “particle” of knowledge. These particles interact according to well-defined rules, and the result of their interaction becomes a computed function. Such a function can have side effects. For example, the result could cause the input or output of a command, a subsequent change of information on a database, or a freshly made HTML web page for automated report.

DFO particles exist within multiple Frames of Reference (FORs). Each FOR is implemented as a metric space, that is, as a set of DFO elements with one or more functions (including always the distance function or metric). Due to the generality of the DFO model, a FOR can also be a DFO and vice versa, depending on their position in the hierarchal space structure. A DFO can be an elementary particle in a higher level FOR, and this FOR could be a DFO of another, higher-level, FOR structure, and so on.

All FORs or DFOs can have different metrics. For example, to define the relationships that exist between DFOs representing physical objects, it is often useful to implement a Euclidean metric, which simply returns the distance between the objects. Such a metric is also useful when studying clusters of data where one correlation function is well known. In other cases, where DFO may represent concepts or ideas, we use different metrics, including the Hamming or Levenstein distance functions. These metrics are also useful in comparing strings.

Consider a set of DFOs with certain goals to accomplish in the QRT Data Domain. First, each DFO would define its higher-level FOR by implementing a “center point,” i.e. (0,0,0). DFOs in that FOR would have a distance function to the center point, and the metric distance would determine their importance or relevance. For instance, the shorter the distance between the DFO and the center point, the more relevant the DFO is to accomplishing the goal. This procedure is implemented on all DFO structures and creates a form of artificial subjectivity in each particle of knowledge. The overall computation of all DFOs within a FOR produces a function that pursues greater objectivity in achieving goals.

How is such a metric actually implemented? There are many different mathematical ways to implement metrics. For example, if the problem cannot be easily defined based on previous methods, the metric function may be implemented as the nth level set of any result-sourcing from a classifier system learning approach. It is extremely common that the problem may not easily be defined and different methods must be adopted in almost every instance. The DFO model is self-adaptable and automatically searches for the best method and the shortest path to accomplish its goal. Since the metric distance between a DFO and FOR is stored as a property of the FOR, it is easy to change metrics. A metric change is the equivalent of asking for a different interpretation of the underlying data. Since metric distances between DFOs (or FORs respectively) are implemented in a hierarchical fashion, one can change perspective on an entire data set (i.e. terabyte size) with great ease. Since DFOs implement class inheritance, such changes may ripple down through various levels of sub-DFOs, causing re-computation of intermediate results in a controlled and natural fashion.

DFOs are capable of self-organization. This follows from the implementation of data and functions as sets of hierarchical objects. For example, if the metric of a FOR is differentiable over the set, data in that set can be concentrated by finding the minimum of the differential in close analogy to physical models. A FOR containing many DFO structures can also contain rules for the creation of new DFOs; for the interaction of its DFOs; for calculating functions between smaller DFOs (including the creation of new objects which embody certain relationships between these smaller DFOs); and so forth.

DFOs are based on a complex structure of parallel relationship. These relationships can be expressed as positive (attraction) or negative (repulsion). The interaction between two DFOs can be to change attributes of the particles themselves, much as in a physical system; an attraction is a function of space, which operates to change the position of objects. A reasonable FOR will implement certain rules of symmetry and conservation among its DFO objects. In this way, the methods of mathematics and physics are used to create a structure in which large-scale computations can be performed.

The DFO model is inherently parallel. Since DFOs are discrete objects, they can be implemented on multiple processor systems and calculations can be performed in parallel. Therefore, DFOs provide a natural model for general parallel computation.

The DFO model is not bound to Turing computable functions. The model conceptually provides methods for implementing quantum computing, should hardware become available to implement such functions. There is no theoretical requirement that either the metric or other functions provided by a frame of reference be Turing computable functions. Any function that can take one or more data structures as arguments can be implemented within the DFO model. In addition, non-local functions (such as certain quantum mechanical logics) can be simulated using a DFO model implemented on a Turing-Church type of processor (i.e., a digital computer). The DFO model is modular and extensible.

That is, a set of computations on one data set can be transformed into another data set and used by the second data set to define a set of new functions, which translate the first FOR into the other. In addition, a FOR can contain rules for logical inference and deduction, which operate on its component DFO objects. That FORs are also considered DFOs for higher-level structures allows for lower level structures to define the properties of data. DFOs can also be used to pose queries on other DFO structures. This means that both the query DFO and the answer DFO would exist within the same FOR structure, until a computation would achieve the goal of relating them. In this manner, the DFO Data Model implements the artificial intelligence of functional and rule-based languages such as Prolog in order to solve posed questions or problems. Also, the DFO Data Model can still retain efficiency of data storage and manipulation.

The DFO model is designed to be efficient and adaptable. That is, it is designed to handle extremely large data sets, on the scales of gigabit and terabit sets, and to provide methods for manipulating such large quantities of data using parallel processing systems. DFO structures can be compiled, that is, reduced from a symbolic form into a compact set of machine instructions, and can also implement the type of continuous restrictions on data to prevent database errors.

1 The term differentiation is used here to mean the generation of a new set whose elements are the discrete difference function over the original set. DFO sets are always finite and non-continuous, and a derivative will generally be taken along changes in one parameter of a DFO (similar to a partial derivative). Distance functions in DFOs, like in all metrics, always return a real number as a value, and thus the finite difference function always has at least one minimum with respect to any parameter of a DFO in a given state. As a practical matter, DFOs have memory and therefore computation of such a function may not always be possible (i.e. may itself change the value of the DFO).


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