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and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished.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

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

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.

A more general kind of sequence-prediction problem--the non-deterministic prediction problem--is defined, and a general methodology for its solution presented. The methodology, called SPARC, employs multiple description models to guide the search for plausible sequence-generating rules. Three different models are presented along with algorithms for instantiating them to discover rules. The instantiation process requires that the initial input sequence be substantially transformed to make explicit important features of the sequence. Four different data transformation operators arc described. The architecture of a system called SPARC/E is presented, which implements most of the methodology for discovering sequence-generating rules in the card game Elcusis. Examples of the execution of SPARC/E are presented.

Search 4. Methods for assigning credit and blame--obtaining a local Performance Standard

In the early days of computing, these goals were central to the new discipline called cybernetics [126], [2]. Over the past two decades, progress toward these goals has come from a variety of fields - notably computer science, psychology, adaptive control theory, pattern recognition, and philosophy. Substantial progress has been made in developing techniques for machine learning in highly restricted environments.

A candidate elimination algorithm has been shown whicn will find all rule versions consistent with all training instances. Backtracking is not required for noise-free training instances, and the final result is independent of the order of presentation of instances. Version spaces provide at once a compact summary of past training instances and a representation of all plausible rule versions. Pecause they provide an explicit representation for the space of plausible rules, version spaces allow a program to represent "how much it doesn't know" about the correct form of the rule. This suggests the utility of the version space approach to problems such as intelligent selection of training instances and merging sets of independently generated rules.

Empirical rule learning and analytic Most learning is based on experience, and this requires a learning methods have predominantly used the first path, representation for the experiential input given to the whereas connectionist systems have relied on the second.

In this paper we propose a framework for supervised and semi-supervised learning based on reformulating the learning problem as a regularized Fredholm integral equation. Our approach fits naturally into the kernel framework and can be interpreted as constructing new data-dependent kernels, which we call Fredholm kernels. We proceed to discuss the noise assumption" for semi-supervised learning and provide evidence evidence both theoretical and experimental that Fredholm kernels can effectively utilize unlabeled data under the noise assumption. We demonstrate that methods based on Fredholm learning show very competitive performance in the standard semi-supervised learning setting."

In recent years, distributed representations of inputs have led to performance gains in many applications by allowing statistical information to be shared across inputs. However, the predicted outputs (labels, and more generally structures) are still treated as discrete objects even though outputs are often not discrete units of meaning. In this paper, we present a new formulation for structured prediction where we represent individual labels in a structure as dense vectors and allow semantically similar labels to share parameters. We extend this representation to larger structures by defining compositionality using tensor products to give a natural generalization of standard structured prediction approaches. We define a learning objective for jointly learning the model parameters and the label vectors and propose an alternating minimization algorithm for learning. We show that our formulation outperforms structural SVM baselines in two tasks: multiclass document classification and part-of-speech tagging.