Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.

Mathematical logic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mathematical logic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.

Mathematical logic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The result of the European Summer Meeting of the Association for Symbolic Logic, this volume gives an overview of the latest developments in most of the major fields of logic being actively pursued today. Important new developments in the applications of logic in computer science are presented. Other areas examined include model theory, set theory, recursion theory, proof theory, and the history of logic. This volume contains the texts of ten of the invited lectures and six of the contributed papers.

Mathematical logic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Logic's basic elements are unfolded in this book. The relation of and the transition from Logic to Logic Programming are analysed. With the use and the development of computers in the beginning of the 1950's, it soon became clear that computers could be used, not only for arithmetical computation, but also for symbolic computation. Hence, the first arithmetical computation programs, and the first programs created to answer elementary questions and prove simple theorems, were written simultaneously. The basic steps towards a general method based on Logic, were accomplished in 1965 by Robinson and later by Kowalski and Colmerauer who made use of Logic directly as a Logic Programming language. Each chapter includes solved as well as unsolved exercises provided to help the reader assimilate the corresponding topics. The solved exercises demonstrate how to work methodically, whereas the unsolved exercises aim to stimulate the reader's personal initiative. The contents of the book are self-contained; only an elementary knowledge of analysis is required. Thus, it can be used by students in every academic year, as simply reading material, or in the context of a course. It can also be used by those who utilize Logic Programming without having any particular theoretical background knowledge of Logic, or by those simply interested in Logic and its applications in Logic Programming.

Mathematical logic