Beyond Turing: a knowledge based model relativistic Cn machine

ABSTRACT

We extend some Turing notions of computation, from over the integers Z, to computation over complex variables C. Corresponding to scientific problems, we implement knowledge based heuristically developed Prolog databases for visualizing and symbolically analyzing domains for analytic functions over several complex variables. The domains, at the outset, deal with the quantum theory of physical fields, incorporating Einstein's special relativity in a 1-space, 1-time model. These methods could constitute the earliest symbolic computer experiments for several complex variable domains. The objects visualized are of dimension 12, with methods to hopefully handle even higher dimensions. The computations are motivated by a formulation of Hilbert's 6'th problem and impact on artificial intelligence capabilities of machines. We use logical deduction and inference, with a form of Minsky frames and slots.

REFERENCES

• Ka: G. Kallen and A. S. Wightman: The Analytic Properties of the Vacuum Expectation Value of a Product of Three Scalar Local Fields. Mat. Fys. Skr. Dan. Vid. Selsk. 1, No. 6 (1958).
• Ma1: A. C. Manoharan and M. Manoharan: Some Artificial Intelligence Methods for Analysis with Several Complex Variables. In: Proceedings of the Second Oklahoma Symposium on Artificial Intelligence p249 (1988), and: Prolog for Computer Analysis of Holomorphic Convexity. In: Proceedings of the Third Oklahoma Symposium on Artificial Intelligence p85 (1989).
• Ma2: A. C. Manoharan, Predicate Calculus for Computer Analysis of Several Complex Variable Domains. In: Proceedings of the ACM South Regional Conference, p142, Nov. (ACM 1989).
• Ma3: A. C. Manoharan, A Complex Projective Space and Analytic Wightman Functions. In: Analytic Methods in Mathematical Physics p487. Gordon and Breach 1970. Indiana International Conference 1968.
• Ma4: A. C. Manoharan: A Funny Thing Happened in the Chinese Room: but How Clever is the Digital Computer? Mountain-Plains Philosophy Conference. (1990).
• Ma5: A. C. Manoharan , M. Manoharan, Simulation of simple computation over a product of several complex number fields (abstract and references only), Proceedings of the 19th annual conference on Computer Science, p.672, April 1991, San Antonio, Texas, United States [doi>10.1145/327164.328839]
• Mc: McCarthy: Speech Acts. Keynote speaker at ACM Annual Comp. Sc. Conf. (1991).
• Mi: M. Minsky: A Framework for Representing Knowledge. (1975). In: Readings in Knowledge Representation. R. J. Brachman and H. J. Levesque (eds.). Morgan Kaufmann (1985).
• Tu: A. Turing: On Computable Numbers with an Application to the Entscheidungsproblem. Proc Lond. Math. Soc. 42, p. 230 (1937) and Computing Machinery and Intelligence, Mind 59, p. 433 (1950)
• Ul: Jeffrey D. Ullman, Principles of database and knowledge-base systems, Vol. I, Computer Science Press, Inc., New York, NY, 1988
• We: Keith Weiskamp , Terry Hengl, Artificial intelligence programming with Turbo Prolog, John Wiley & Sons, Inc., New York, NY, 1988
• Wi: A. S. Wightman: Hilbert's Sixth Problem: Mathematical Treatment of the Axioms of Physics. Proceedings of Symposia in Pure Mathematics 28. p. 147. (1976). American Mathematical Society.

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.1 COMPUTATION BY ABSTRACT DEVICES
      F.1.1 Models of Computation
          Subjects: Bounded-action devices (e.g., Turing machines, random access machines)

Additional Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Physics

General Terms:
Theory