Foundations Logic Language And Mathematics
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Foundations: Logic, Language, and Mathematics
Author: Hugues Leblanc
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
The more traditional approaches to the history and philosophy of science and technology continue as well, and probably will continue as long as there are skillful practitioners such as Carl Hempel, Ernest Nagel, and th~ir students. Finally, there are still other approaches that address some of the technical problems arising when we try to provide an account of belief and of rational choice. - These include efforts to provide logical frameworks within which we can make sense of these notions. This series will attempt to bring together work from all of these approaches to the history and philosophy of science and technology in the belief that each has something to add to our understanding. The volumes of this series have emerged either from lectures given by authors while they served as honorary visiting professors at the City College of New York or from conferences sponsored by that institution. The City College Program in the History and Philosophy of Science and Technology oversees and directs these lectures and conferences with the financial aid of the Association for Philosophy of Science, Psychotheraphy, and Ethics. MARTIN TAMNY RAPHAEL STERN PREFACE The papers in this collection stem largely from the conference 'Foun dations: Logic, Language, and Mathematics' held at the Graduate Center of the City University of New York on 14-15 November 1980.
Foundations of Logic and Mathematics
This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Mathematical Logic
Author: Wei Li
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-02-26
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.