Other Research

* Natural-Language Legal Expert System Builder (NLESB)
* The Calculus of Functional Differences
* Lp Circular Functions
* Evolutionary Neurotheology, Jungian Psychology, & Neoplatonism
* Biographies of Greek Philosophers

Natural-Language Legal Expert System Builder (NLESB)

NLESB enables a lawyer to build a useful legal expert system in ordinary English without being a computer expert. It accepts rules in ordinary English, though in normalized form, and parses them into propositional data structures that it can use to draw inferences. NLESB has some features, particularly in its logic, that are peculiar to the needs of legal expert systems.

Send me mail for reprints or if you are interested in using our prototype implementation.

Publications (reverse chronological order):

  1. “A Logic for Statutory Law,” by John Nolt, Grayfred B. Gray, Bruce J. MacLennan, and Donald J. Ploch, Jurimetics 35, 2 (Winter 1995), pp. 121–151. Winner of Loevinger Prize.

  2. “Legal Expert System Building: A Semi-Intelligent Computer Program Makes It Easier,” by Grayfred B. Gray, Bruce J. MacLennan, John E. Nolt & Donald R. Ploch, John Marshall Journal of Computer and Information Law, 12 (1994), pp. 555–583.

  3. “Readability of the Law: Forms of Law for Building Legal Expert Systems,” by Donald R. Ploch, Bethany K. Dumas, Grayfred B. Grey, Bruce J. MacLennan, and John E. Nolt, Jurimetrics 33, 2 (Winter 1993), pp. 189–221.

  4. “Law Reading Experiment,” by Donald R. Ploch, Bethany K. Dumas, Grayfred H. Gray, Bruce MacLennan, & John Nolt, Pre-Proceedings of the III International Conference, Logica Informatica Diritto: Legal Expert Systems, A. A. Martino (ed.), Consiglio Nazionale delle Ricerche, Istituto per la documentazione giuridica, Florence, Italy, November 2-5, 1989, Vol. 2, pp. 681–704.

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Miscellaneous

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“A Calculus of Functional Differences” [compressed postscript]

Abstract: Functions can often be defined by recursive equations such as these:

   f(x) = b(x),     if p(x)
f[h(x)] = gx[f(x)], otherwise.
The second equation says that if the input to f “varies” by h, then its output “varies” by gx. We call this a functional difference equation; it is analogous to a numerical difference equation, such as:
f(h + x) = gx + f(x),
which says that the output of f varies by gx when its input is varied by h. Since in our theory we vary the input by an arbitrary function, rather than a numerical displacement, we can take differences of functions defined on nonnumeric domains, such as lists, trees and sets.

The ultimate goal of this research is to improve our ability to reason about functional programs. Specifically, the theory of functional differences provides a means of going from local descriptions of behavior (difference equations) to global descriptions (the solution to the difference equation), and vice versa.

In this paper we define several different kinds of functional differences and present fundamental results concerning them (existence, uniqueness, etc.). We also present a complementary operation of “functional integration” that can be used to solve functional difference equations.

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“Lp Circular Functions” (Jan '93 version [pdf], which corrects Table 1 in May '92 version [compressed postscript]):

Abstract: In this report we develop the basic properties of a set of functions analogous to the circular and hyperbolic functions, but based on Lp circles, thus a kind of generalized trigonometry. The resulting identities may simplify analysis in Lp spaces in much the way that the circular functions do in Euclidean space. In any case, they are a pleasing example of mathematical generalization.

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Evolutionary Neurotheology, Jungian Psychology, & Neoplatonism

  1. “Evolutionary Neurotheology and the Varienties of Religious Experience” [html, pdf, rtf] -- an extended version of a chapter in NeuroTheology: Brain, Science, Spirituality, Religious Experience, R. Joseph (Ed.), University Press, California, 2002.

  2. Evolution, Jung, and Theurgy: Their Role in Modern Neoplatonism:

  3. “Evolutionary Jungian Psychology” [pdf (1 MB)], Psychological Perspectives 49, 1 (Spring 2006), pp. 9–28.

  4. “Neoplatonism in Science: Past and Future” [pdf (196 KB)], extended version of paper [pdf (212 KB)] presented at International Society for Neoplatonic Studies meeting, New Orleans, June 22–26, 2005, and to appear in Metaphysical Patterns in Platonism:  Ancient, Medieval, Renaissance, and Modern, edited by J. Finamore & B. Berchman, University Press of the South, in press, pp. 441–59.  Both versions revised July 17, 2006. 

  5. “Individual Soul and World Soul: The Process of Individuation in Neoplatonism & Jung” [pdf (1.8 MB)], invited chapter for Thomas Arzt & Axel Holm (Eds.), Wegmarken der Individuation (Milestones of Individuation). Würzburg: Königshausen & Neumann, 2006, pp. 83–116.

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Biographies of ancient Greek philosophers:  Apuleius of Madauros (ch. 46, pp. 207–9) and Iamblichus of Chalcis (ch. 50, pp. 223–6), extended versions of two biographies for Meet the Philosophers of Ancient Greece, ed. Patricia O'Grady, Aldershot: Ashgate, 2005.

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Send mail to Bruce MacLennan / MacLennan@utk.edu

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Last updated: 2007-12-15.