A. YONEZAWA and C. HEWITT 41 REPRESENTATIONS FOR ABSTRACT REASONING 4 A maximal method for set variables in automatic theorem-proving W. W. BLEDSOE

The two outstanding figures in the history of computer science are Alan Turing and John von Neumann, and they shared the view that logic was the key to understanding and automating computation. In particular, it was Turing who gave us in the mid-1930s the fundamental analysis, and the logical definition, of the concept of'computability by machine' and who discovered the surprising and beautiful basic fact that there exist universal machines which by suitable programming can be made to t This essay is an expanded and revised version of one entitled The Role of Logic in Computer Science and Artificial Intelligence, which was completed in January 1992 (and was later published in the Proceedings of the Fifth Generation computer Systems 1992 Conference). Since completing that essay I have had the benefit of extremely helpful discussions on many of the details with Professor Donald Michie and Professor I. J. Good, both of whom knew Turing well during the war years at Bletchley Park. Professor J. A. N. Lee, whose knowledge of the literature and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished. Further light has very recently been shed on the von Neumann side of the story by Norman Macrae's excellent biography John von Neumann (Macrae 1992). Accordingly, it seemed appropriate to undertake a more complete and thorough version of the FGCS'92 essay, focussing somewhat more on the interesting historical and biographical issues. I am grateful to Donald Michie and Stephen Muggleton for inviting me to contribute such a'second edition' to the present volume, and I would also like to thank the Institute for New Computer Technology (ICOT) for kind permission to make use of the FGCS'92 essay in this way. 1 LOGIC, COMPUTERS, TURING, AND VON NEUMANN

The aim of the Stat Log project is to compare the performance of statistical, machine learning, and neural network algorithms, on large real world problems. This paper describes the completed work on classification in the StatLog project. Classification is here defined to be the problem, given a set of multivariate data with assigned classes, of estimating the probability from a set of attributes describing a new example sampled from the same source that it has a pre-defined class. We gathered together a representative collection of algorithms from statistics (Naive Bayes, K-nearest Neighbour, Kernel density, Linear discriminant, Quadratic discriminant, Logistic regression, Projection pursuit, Bayesian networks), machine learning (CART, C4.5, NewID, AC2, CAL5, CN2, ITrule -- only propositional symbolic algorithms were considered), and neural networks (Backpropagation, Radial basis functions, Kohonen).

When you lose a game of chess to a computer then don't pretend that you didn't think at the game.

Bayesian inference nets 190 algorithms, structure-moving task 209-17 Kononenko's treatment 201-2 ALG(SIG, E) 50

In this paper we will be concerned with such reasoning in its most general form, that is, in inferences that are defeasible: given more information, we may retract them. The purpose of this paper is to introduce a form of non-monotonic inference based on the notion of a partial model of the world. We take partial models to reflect our partial knowledge of the true state of affairs. We then define non-monotonic inference as the process of filling in unknown parts of the model with conjectures: statements that could turn out to be false, given more complete knowledge. To take a standard example from default reasoning: since most birds can fly, if Tweety is a bird it is reasonable to assume that she can fly, at least in the absence of any information to the contrary. We thus have some justification for filling in our partial picture of the world with this conjecture. If our knowledge includes the fact that Tweety is an ostrich, then no such justification exists, and the conjecture must be retracted.

This paper describes some work on automatically generating finite counterexamples in topology, and the use of counterexamples to speed up proof discovery in intermediate analysis, and gives some examples theorems where human provers are aided in proof discovery by the use of examples.

K.A.PATON 411 24 Centromere finding: some shape descriptors for small chromosome outlines.

General problems in analyzing information in a probabilistic database are considered.

Arguments are presented in favor of the answer "yes". The intuitive appeal (or lack thereof) of probabilities is considered briefly. The theoretical adequacies of probabilistic methods are investigated by considering them in light of McCarthy's "typology of uses of non-monotonic reasoning." A quantitative approach which overcomes the usual need for a priori probabilities is presented. Some of the practical advantages of using probabilities in a production system are described.