Perspectives On The History Of Mathematical Logic
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Author | : Thomas Drucker |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2009-05-21 |
Genre | : Mathematics |
ISBN | : 0817647694 |
This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.
Author | : Thomas Drucker |
Publisher | : Birkhauser |
Total Pages | : 195 |
Release | : 1991-01-01 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : 9783764334444 |
Author | : Vincenzo De Risi |
Publisher | : Springer Nature |
Total Pages | : 304 |
Release | : 2020-01-01 |
Genre | : Science |
ISBN | : 3030255727 |
The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.
Author | : Radim Bělohlávek |
Publisher | : Oxford University Press |
Total Pages | : 545 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 0190200014 |
The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.
Author | : Donald W. Loveland |
Publisher | : Princeton University Press |
Total Pages | : 344 |
Release | : 2014-01-26 |
Genre | : Mathematics |
ISBN | : 140084875X |
Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
Author | : G. T. Kneebone |
Publisher | : Dover Publications |
Total Pages | : 0 |
Release | : 2001 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : 9780486417127 |
Ideal for students intending to specialize in the topic. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics. Part III focuses on the philosophy of mathematics.
Author | : Jean van Heijenoort |
Publisher | : Harvard University Press |
Total Pages | : 684 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : 9780674324497 |
Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel.
Author | : Jörg Flum |
Publisher | : Amsterdam University Press |
Total Pages | : 737 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9053565760 |
Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d’horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field.
Author | : Alexander Prestel |
Publisher | : Springer Science & Business Media |
Total Pages | : 198 |
Release | : 2011-08-21 |
Genre | : Mathematics |
ISBN | : 1447121767 |
Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Author | : F.D. Kamareddine |
Publisher | : Springer Science & Business Media |
Total Pages | : 367 |
Release | : 2006-03-10 |
Genre | : Mathematics |
ISBN | : 1402023359 |
This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.