Download or read book The De mathematisation of Logic written by Barry Hartley Slater and published by Polimetrica s.a.s.. This book was released on 2007 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Logical Approach to Discrete Math written by David Gries and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.
Download or read book The Mathematical Analysis of Logic written by George Boole and published by . This book was released on 1847 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Analysis of Logic by George Boole, first published in 1948, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Download or read book Mathematics and Logic written by Mark Kac and published by Courier Corporation. This book was released on 1992-01-01 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
Download or read book Logic for Mathematicians written by A. G. Hamilton and published by Cambridge University Press. This book was released on 1988-09-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Logic for Mathematicians, author Hamilton introduces the reader to the techniques and principle results of mathematical logic.
Download or read book The Algebra of Logic written by Louis Couturat and published by . This book was released on 1911 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Beginner s Guide to Mathematical Logic written by Raymond M. Smullyan and published by Courier Corporation. This book was released on 2014-07-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com
Download or read book A Beginner s Further Guide to Mathematical Logic written by Raymond Smullyan and published by World Scientific Publishing Company. This book was released on 2016-11-11 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan. This book is a sequel to my Beginner's Guide to Mathematical Logic. The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results. The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a "fein" chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a "decision machine." Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic. This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics. Request Inspection Copy
Download or read book What is Mathematical Logic written by John N. Crossley and published by Courier Corporation. This book was released on 1990-01-01 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the main ideas and results of mathematical logic is a serious treatment geared toward non-logicians. Starting with a historical survey of logic in ancient times, it traces the 17th-century development of calculus and discusses modern theories, including set theory, the continuum hypothesis, and other ideas. 1972 edition.
Download or read book Elements of Mathematical Logic written by Jan Łukasiewicz and published by . This book was released on 1966 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction To Mathematical Logic Extended Edition written by Michal Walicki and published by World Scientific Publishing Company. This book was released on 2016-08-12 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.
Download or read book A Course in Mathematical Logic written by I͡U. I. Manin and published by Springer Science & Business Media. This book was released on 1977 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems.
Download or read book Mathematical Logic written by Ian Chiswell and published by OUP Oxford. This book was released on 2007-05-18 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
Download or read book Perspectives on the History of Mathematical Logic written by Thomas Drucker and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Mathematical Logic written by Elliot Mendelsohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Download or read book Logic as Algebra written by Paul Halmos and published by Cambridge University Press. This book was released on 1998-09-03 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to logic from the perspective of algebra.
Download or read book The Algebra of Logic written by Louis Couturat and published by . This book was released on 2019-08-24 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Logic is a necessary preliminary to logical Mathematics. MathematicalLogic is the name given by Peano to what is also known (afterVenn ) as Symbolic Logic; and Symbolic Logic is, in essentials, the Logicof Aristotle, given new life and power by being dressed up in the wonderfulalmost magicalarmour and accoutrements of Algebra. In less than seventyyears, logic, to use an expression of De Morgan's, has so thriven upon symbolsand, in consequence, so grown and altered that the ancient logicians wouldnot recognize it, and many old-fashioned logicians will not recognize it. Themetaphor is not quite correct: Logic has neither grown nor altered, but we nowsee more of it and more into it.
