Mathematical logic

This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history.

The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science.

This book is designed for use in a one semester problem-oriented course in undergraduate set theory.

It is Sunday, the 7th of September 1930.

In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con- sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH.

Since its inception by Professor Lotfi Zadeh about 18 years ago, the theory of fuzzy sets has evolved in many directions, and is finding applications in a wide variety of fields in which the phenomena under study are too complex or too ill-defined to be analyzed by conventional techniques.

This book presents a selection of papers presented to the Second Inter- national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998.

Rough Sets and Data Mining: Analysis of Imprecise Data is an edited collection of research chapters on the most recent developments in rough set theory and data mining.

As understanding of the engineering design and configuration processes grows, the recognition that these processes intrinsically involve imprecise information is also growing.

Fuzzy Logic Foundations and Industrial Applications is an organized edited collection of contributed chapters covering basic fuzzy logic theory, fuzzy linear programming, and applications.

Fuzzy Modelling: Paradigms and Practice provides an up-to-date and authoritative compendium of fuzzy models, identification algorithms and applications.

This volume presents the results of approximately 15 years of work from researchers around the world on the use of fuzzy set theory to represent imprecision in databases.

Introduction to Fuzzy Reliability treats fuzzy methodology in hardware reliability and software reliability in a relatively systematic manner.

As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate.

IN 1959 I lectured on Boolean algebras at the University of Chicago.

Primarily, this book addresses beginning graduate students expecting to become mathematicians or mathematically oriented computer scientists.

In 1965 Juris Hartmanis and Richard E.

For Students Congratulations!

Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions.

Descriptive set theory has been one of the main areas of research in set theory for almost a century.

In mathematics there are limits, speed limits of a sort, on how many computational steps are required to solve certain problems.

The volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences.

Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science.

There are many kinds of books on formal logic.

The geometric calculus, in general, consists in a system of operations on geometric entities, and their consequences, analogous to those that algebra has on the num- bers.

In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for- mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "e;transition"e; course, rather than in traditional courses such as linear algebra.

Real analytic sets in Euclidean space (Le.

This volume contains papers which are based primarily on talks given at an inter- national conference on Algorithmic Problems in Groups and Semigroups held at the University of Nebraska-Lincoln from May ll-May 16, 1998.

This monograph develops techniques for equational reasoning in higher-order logic.

The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory.

This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "e;Application and Theory of Random Sets.

Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space.

In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re- cent dramatic growth in the applications oflogic to computer science.

A basic issue in computer science is the complexity of problems.

This monograph studies the logical aspects of domains as used in de- notational semantics of programming languages.

In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig- inated by Herbrand and developed in the case of standard first-order unifi- cation by Martelli and Montanari.

We dedicate this book to the memory of J.

This book provides an account of those parts of contemporary set theory of direct relevance to other areas of pure mathematics.

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science.

The study of the connections between mathematical automata and for- mal logic is as old as theoretical computer science itself.

The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work.

1.

The idea for this book was conceived over the second bottle of Villa Maria's Caber- net Medot '89, at the dinner of the Australasian Combinatorics Conference held at Palmerston North, New Zealand in December 1990, where the authors first met and discovered they had a number of interests in common.

The theory of finite automata on finite stings, infinite strings, and trees has had a dis- tinguished history.

This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: * Why is the truth table for the logical implication so unintuitive?

This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets.

Logic is, and should be, the core subject area of modern mathemat- ics.

Lewis Carroll the author of the world famous Alice in Wonderland is well known even today for his fiction, but his tenure as professor of mathematics at Oxford university is less well known as is his love of logic problems.