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 Logic & Formal Reasoning


Letter to the Editor

AI Magazine

One to organize the construction teams. One to hack the planning system. How many AI people does it take to change a lightbulb? One to get Westinghouse to sponsor the research. One to indicate about how the robot mimics human motor A. At least 55: The knowledge engineering group (6): One to define the goal state.


I Had a Dream: AAAI Presidential Address

AI Magazine

Twenty-five years ago I had a dream, a daydream, if you will. A dream shared with many of you. I dreamed of a special kind of computer, which had eyes and ears and arms and legs, in addition to its "brain." I did not dream that this new computer friend would be a means of making money for me or my employer or a help for my country - though I loved my country then and still do, and I have no objection to making money. I did not even dream of such a worthy cause as helping the poor and handicapped of the world using this marvelous new machine. No, my dream was filled with the wild excitement of seeing a machine act like a human being, at least in many ways.


Automata--theoretic techniques for modal logic of programs

Classics

We present a new technique for obtaining decision procedures for modal logics of programs. The technique centers around a new class of finite automata on infinite trees for which the emptiness problem can be solved in polynomial time. The decision procedures then consist of constructing an automaton Af for a given formula f such that Af accepts some tree if and only if f is satisfiable. We illustrate our technique by giving exponential decision procedures for several variants of deterministic propositional dynamic logic.


Proof-Checking Metamathematics

Classics

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.


Logic for Computer Science: Foundations of Automatic Theorem Proving

Classics

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."





Artificial Intelligence Research at the University of California, Los Angeles

AI Magazine

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.


Artificial Intelligence Research at the University of California, Los Angeles

AI Magazine

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.