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Logical Writings
In 1968 Jean van Heijenoort published an edition of Herbrand's collected logic papers (Herbrand 1968). The core of the present volume comprises translations of these papers and of the biographical notes also appearing in that edition. With two exceptions, this is their first appearance in English; the exceptions are Chap. 5 of Herbrand's thesis and Herbrand 1931c, both of which appeared in van Heijenoort 1967, the former trans lated by Burton Dreben and van Heijenoort, and the latter by van Heijenoort. These two translations have been reprinted here, thanks to the permission ofthe Harvard University Press, with only minor changes. The remainder of the present translations are my own; I am gr...
Philosophy of Mathematics
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathe...
Foundations of Information and Knowledge Systems
This book constitutes the refereed proceedings of the First International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2000, held in Burg, Germany, in February 2000. The 14 revised full papers and four short papers were carefully reviewed and selected from a total of 45 submissions. Among the topics addressed are logical foundations and semantics of datamodels, dependency theory, integrity and security, temporal aspects, foundations of information systems design including Web-based information services, and query languages and optimization.
Logic and Computational Complexity
This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.
Logic from Russell to Church
This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.• The entire range of modal logic is covered• Serves as a singular contribution to the intellectual history of the 20th century• Contains the latest scholarly discoveries and interpretative insights
Elementary and Analytic Theory of Algebraic Numbers
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Neural-Symbolic Cognitive Reasoning
This book explores why, regarding practical reasoning, humans are sometimes still faster than artificial intelligence systems. It is the first to offer a self-contained presentation of neural network models for many computer science logics.
Logic Programming
This book constitutes the refereed proceedings of the 20th International Conference on Logic Programming, ICLP 2004, held in Saint-Malo, France in September 2004. The 28 revised full papers and 16 poster papers presented together with 2 invited papers were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on program analysis, constraints, alternative programming paradigms, answer set programming, and implementation.
A Classical Introduction to Modern Number Theory
This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any ...
PROCEEDINGS OF THE 21ST CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2021
Our life is dominated by hardware: a USB stick, the processor in our laptops or the SIM card in our smart phone. But who or what makes sure that these systems work stably, safely and securely from the word go? The computer - with a little help from humans. The overall name for this is CAD (computer-aided design), and it’s become hard to imagine our modern industrial world without it. So how can we be sure that the hardware and computer systems we use are reliable? By using formal methods: these are techniques and tools to calculate whether a system description is in itself consistent or whether requirements have been developed and implemented correctly. Or to put it another way: they can b...
