LT revisited : explanation-based learning and the logic of Principia mathematica

This paper describes an explanation-based learning (EBL) system based on a version of Newell, Shaw and Simon's LOGIC-THEORIST (LT). Results of applying this system to propositional calculus problems from Principia Mathematica are compared with results of applying several other versions of the same performance element to these problems. The primary goal of this study is to characterize and analyze differences between not learning, rote learning (LT's original learning method), and EBL. Another aim is to provide base-line characterizations of the performance of a simple problem solver in the context of the Principa problems, in the hope that these problems can be used as a benchmark for testing improved learning methods, just as problems like chess and the eight puzzle have been used as benchmarks in research on search methods

The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problems

In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random impurities, level crossing transitions in the chiral Potts model and the use of Rogers-Ramanujan identities to generalize our concepts of Bose/Fermi statistics. Each of these advances has led to the further discovery of major unsolved problems of great mathematical and physical interest. I will here discuss the mathematical advances, the physical insights and extraordinary lack of visibility of this field of physics.Comment: Text of the 1999 Heineman Prize address given March 24 at the Centenial Meeting of the American Physical Society in Atlanta 20 pages in latex, references added and typos correcte

On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are {\it gauge variables}, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the {\it Dirac observables}, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of {\it causality} dictates the choice of {\it retarded} solutions at the classical level. However both the problems of the classical theory of the electron, leading to the choice of ${1\over 2} (retarded + advanced)$ solutions, and the regularization of quantum field teory, leading to the Feynman propagator, introduce {\it anticipatory} aspects. The determination of the relativistic Darwin potential as a semi-classical approximation to the Lienard-Wiechert solution for particles with Grassmann-valued electric charges, regularizing the Coulomb self-energies, shows that these anticipatory effects live beyond the semi-classical approximation (tree level) under the form of radiative corrections, at least for the electro-magnetic interaction.Comment: 12 pages, Talk and "best contribution" at The Sixth International Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16, 200

Separability and distillability in composite quantum systems -a primer-

Quantum mechanics is already 100 years old, but remains alive and full of challenging open problems. On one hand, the problems encountered at the frontiers of modern theoretical physics like Quantum Gravity, String Theories, etc. concern Quantum Theory, and are at the same time related to open problems of modern mathematics. But even within non-relativistic quantum mechanics itself there are fundamental unresolved problems that can be formulated in elementary terms. These problems are also related to challenging open questions of modern mathematics; linear algebra and functional analysis in particular. Two of these problems will be discussed in this article: a) the separability problem, i.e. the question when the state of a composite quantum system does not contain any quantum correlations or entanglement and b) the distillability problem, i.e. the question when the state of a composite quantum system can be transformed to an entangled pure state using local operations (local refers here to component subsystems of a given system). Although many results concerning the above mentioned problems have been obtained (in particular in the last few years in the framework of Quantum Information Theory), both problems remain until now essentially open. We will present a primer on the current state of knowledge concerning these problems, and discuss the relation of these problems to one of the most challenging questions of linear algebra: the classification and characterization of positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod. Optics, minor typos corrected, references adde