While program verification was always a. desirable, but never an easy task, the advent of concurrent

Formal proof-checking has long been recognized as an interesting application of computers. It has often been claimed that significant proofs in mathematics cannot be checked using an automatic proof-checker, and that formal proofs lack the intuitive plausibility and insight that informal proofs possess. We argue against these claims by presenting machine-checked versions of some landmark proofs in metamathematics, such as those of the tautology theorem, Godel's incompleteness theorem, and the Church-Rosser theorem. These proofs were checked using the Boyer-Moore theorem power. The tautology theorem and the incompleteness theorem are proved by first defining a proof-checker for the formal theory Z2 in the Boyer-Moore logic.

This book is a new addition to the Harper & Row Computer Science and Technology Series, and is intended for senior undergraduates or first-year graduate students. It is an introduction to mathematical logic, with some computer science applications. The first chapter sets the goals for the book, which include explanations of proof theory, model theory, and automatic theorem providing for those formulas that are true. The second chapter is designed as an introduction for the novice to those mathematical concepts used throughout the rest of the book. The author says, "This fairly lengthy chapter has been included in order to make this book as self-contained as possible. Readers with a firm mathematical background may skim or even skip this chapter entirely."

Home Conferences MOD Proceedings PODS '86 Magic sets and other strange ways to implement logic programs (extended abstract)

Research in AI within the Computer Science Department at the University of California, Los Angeles is loosely composed of three interacting and cooperating groups: (1) the Artificial Intelligence Laboratory, at 3677 Boelter Hall, which is concerned mainly with natural language processing and cognitive modelling, (2) the Cognitive Systems Laboratory, at 4731 Boelter Hall, which studies the nature of search, logic programming, heuristics, and formal methods, and (3) the Robotics and Vision Laboratory, at 3532 Boelter Hall, where research concentrates on robot control in manufacturing, pattern recognition, and expert systems for real-time processing.

Research in AI within the Computer Science Department at the University of California, Los Angeles is loosely composed of three interacting and cooperating groups: (1) the Artificial Intelligence Laboratory, at 3677 Boelter Hall, which is concerned mainly with natural language processing and cognitive modelling, (2) the Cognitive Systems Laboratory, at 4731 Boelter Hall, which studies the nature of search, logic programming, heuristics, and formal methods, and (3) the Robotics and Vision Laboratory, at 3532 Boelter Hall, where research concentrates on robot control in manufacturing, pattern recognition, and expert systems for real-time processing.

About a year ago. I was approached by Phoebe Huang of Comtex Scientific Corporation who hoped that I would help devise a dramatically expanded index for topics in AI to aid Comtex in indexing the series of AI memos and reports that they had been gathering. Comtex had tried to get the ACM to expand and update its classification. But was told that ACM had just revised the listing two years ago or so ago, and did not intend to revise it again for a while: even if they did. The revision might require a year or more to complete. Comtex wanted the new classification within six to eight weeks. I agreed to take on the task, thinking it wouldn't be too hard. The major decision I had to make was whether to use the existing ACM index scheme and add to it, or start with a fresh sheet of paper and devise my own. I decided to stick with ACM's top two levels, only adding, not modifying, major headings.

In Defense of Probability Peter Cheeseman SRI International 333 Ravenswood Ave., Menlo Park, California 94025 Abstract In this paper, it is argued that probability theory, when used correctly, is suffrcient for the task of reasoning under uncertainty. Since numerous authors have rejected probability as inadequate for various reasons, the bulk of the paper is aimed at refuting these claims and indicating the scources of error. In particular, the definition of probability as a measure of belief rather than a frequency ratio is advocated, since a frequency interpretation of probability drastically restricts the domain of applicability. Other sources of error include the confusion between relative and absolute probability, the distinction between probability and the uncertainty of that probability. Also, the interaction of logic and probability is discusses and it is argued that many extensions of logic, such as "default logic" are better understood in a probabilistic framework. The main claim of this paper is that the numerous schemes for representing and reasoning about uncertainty that have appeared in the AI literature are unnecessary--probability is all that is needed. 1 Introduction A glance through any major AI publication shows that an overwhelming proportion of papers are concerned with what might be described as the logical approach to inference and knowledge representation. It now widely accepted that many knowledge representations can be mapped into (first order) predicate calculus, and the corresponding inference procedures can be reduced to a type of controlled logical deduction. However, examples of human reasoning (judgements) are full of such terms as "probably", "most", "usually" etc., showing that many patterns of human reasoning are not logical in form, but intrinsically probabilistic. The claim that many patterns of human reasoning are probabilistic does not mean that the underlying "logic" of such patterns cannot be axiomatized. On the contrary, a basis for such an axiomatization is given in section 3. The claim is that when such an exercise is performed, the resulting patterns of inference are different in form from those found in analogous logical deductions.

Founded early in 1983, the center for the Study of Language and Information (CSLI) at Stanford University grew out of a long-standing collaboration between scientists at research laboratories in the Palo Alto area and the faculty and students of several Stanford University departments and out of a need for an institutional focus for this work on natural and computer languages. At present, CSLI has 17 senior members and about as many associate members, from SRI International, Xerox PARC, Fairchild, and the Department of Computer Science, Linguistics, and Philosophy at Stanford. Since the Center's research will overlap with the work of other researchers around the world, an important goal of CSLI is to initiate a major outreach, whereby members of CSLI both inform themselves of work done elsewhere and share their own results with others.

Charles A. Rosen came to SRI in 1957. I arrived in 1961. Between these dates, Charlie organized an Applied Physics Laboratory and became interested in "learning machines" and "self-organizing systems." That interest launched a group that ultimately grew into a major world center of artificial intelligence research - a center that has endured twenty-five years of boom and bust in fashion, has "graduated" over a hundred AI research professionals, and has generated ideas and programs resulting in new products and companies as well as scientific articles, books, and this particular collection itself.