Naval Intelligent Authentication and Support Through Randomization and Transformative Search

Abstract

The problem addressed, in this chapter, pertains to how to represent and apply knowledge to best facilitate its extension and use in problem solving. Unlike deductive logics (e.g., the predicate calculus), an inherent degree of error is allowed for so as to greatly enlarge the inferential space. This allowance, in turn, implies the application of heuristics (e.g., multiple analogies) to problem solving as well as their indirect use in inferring the heuristics themselves. This chapter is motivated by the science of inductive inference. Examples of state-space search, linguistic applications, and a focus methodology for generating novel knowledge (components) for wartime engagement for countering (cyber) threats (WAMS) are provided.

Appendices

Appendix I: The 3-2-1 Skew

The 3-2-1 skew is a simple (fast) methodology for assigning knowledge relative weights on the basis of Denning’s principle of temporal locality [23]. More recent knowledge tends to be proportionately more valuable. This skew is used to increase the likelihood of solving a problem by taking full advantage of the current operational domain profile (Fig. 3.3).

Fig. 3.3

The 3-2-1 skew for dynamic selection in a case-base segment

Knowledge is acquired at the logical head and moved there when fired. It is also expunged from the logical tail when necessary to release space. The selection of a particular skew is domain specific. For example, the rate of radioactive decay is known to be proportional to how much radioactive material is left (excluding the presence of certain metals). The nuclear decay equation may be used as a skew for various radioactive materials and is given by $A(t) = A_{0} e^{ - \lambda t}$. Here, A(t) is the quantity of radioactive material at time t, and A₀ = A(0) is the initial quantity. $\lambda$ (lambda) is a positive number (i.e., the decay constant) defining the rate of decay for the particular radioactive material. A countably infinite number of other skews may be applicable.

In the following assignment of skew-weights, the skew vector, S, favors the logical head of the case base in keeping with temporal locality. Cases, which were most-recently acquired or fired, and thus appear at or nearer to the logical head of a case-base, are proportionately more heavily weighted under the 3-2-1 skew. Of course, this differs from a uniform skew. The closer a case is to the top of its linked list, the greater its weight or importance. A heuristic scheme (i.e., the 3-2-1 skew) for achieving this with a dependency category consisting of d rules is to assign the head case a weight of $\frac{2d}{d(d + 1)}$. The map just below the head map has a weight of $\frac{2(d - 1)}{d(d + 1)}$.

Finally, the tail map of the segmented case base has a weight of $\frac{2}{d(d + 1)}$. The ith map from the head has a weight of $\frac{2(d - i + 1)}{d(d + 1)}$, for i = 1, 2, …, d. For example, using a vector of four weights, the 3-2-1 skew (S) is S = (0.4, 0.3, 0.2, 0.1)^T. There are a countably infinite number of possible skews, such that $\sum {s_{k} } = 1.0$.

The evaluation of the members of a dependency category is the contiguous weighted sum of its constituent elements. A 3-2-1 skew is defined where the ith map from the head has a weight of $\frac{2(d - i + 1)}{d(d + 1)}$, for i = 1, 2, …, d; where, d specifies the number of terms in the skew. The use of the 3-2-1 skew is optional (i.e., in comparison with uniform weighting) and is useful for domains where the value of the data deteriorates in linear proportion to its time of collection—valuing more recent data, more highly [27]. The use of additional time-dependent weights, depending on whether there is an additional time dependency of the value of the knowledge, is also possible.

Appendix II: Performer Capabilities

Stuart H. Rubin, PI, received a Ph.D. in Computer and Information Science from Lehigh University in 1988. He was previously an ONT Post-Doctoral Fellow, at NOSC, for 3 years and a tenured associate professor of computer science at Central Michigan University. He has over 30 Assigned Navy Patents, over 287 Refereed Publications, and received SSC-PAC’s Publication of the Year Awards in 2007, 2009, 2010, and 2011. He is a SIRI Fellow and serves in leadership roles in numerous IEEE technical societies.

Thouraya Bouabana Tebibel received a Ph.D. in Computer Science from USTHB University (Algeria) in collaboration with Pierre & Marie Curie University (France) in 2007. She has been an engineer/researcher for eight years and is now a full professor of computer science at Ecole Nationale Supérieure d’Informatique in Algeria. She has over 80 refereed publications and a book edited by Editions Universitaires Européennes. She has successfully conducted numerous research projects and supervised 30 BS, 17 MS, and 4 Ph.D. theses.