Aspects Of Mathematical Logic

Author : Paul C. Rosenbloom
Publisher : Courier Dover Publications
Page : 0 pages
File Size : 46,8 Mb
Release : 2005
Category : Logic, Symbolic and mathematical
ISBN : 0486446174

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The Elements of Mathematical Logic by Paul C. Rosenbloom Pdf

An excellent introduction to mathematical logic, this book provides readers with a sound knowledge of the most important approaches to the subject, stressing the use of logical methods in attacking nontrivial problems. Its chapters cover the logic of classes (including a section on the structure and representation of Boolean algebras, which are applied in the following chapters to the study of deductive systems), the logic of propositions, the logic of propositional functions (summarizing the methods of Russell, Quine, Zermelo, Curry, and Church for the construction of such logics), and the general syntax of language, with a brief introduction that also illustrates applications to so-called undecidability and incompleteness theorems. Other topics include the simple proof of the completeness of the theory of combinations, Church's theorem on the recursive unsolvability of the decision problem for the restricted function calculus, and the demonstrable properties of a formal system as a criterion for its acceptability.

Author : Georg Kreisel,Jean Louis Krivine
Publisher : Elsevier
Page : 222 pages
File Size : 54,6 Mb
Release : 1967
Category : Electronic books
ISBN : 0444534121

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Elements of Mathematical Logic by Georg Kreisel,Jean Louis Krivine Pdf

Author : Pascal Hitzler,Anthony Seda
Publisher : CRC Press
Page : 307 pages
File Size : 44,8 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781000218725

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Mathematical Aspects of Logic Programming Semantics by Pascal Hitzler,Anthony Seda Pdf

Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.

Author : Jerzy Słupecki,Ludwik Borkowski
Publisher : Pergamon
Page : 374 pages
File Size : 48,5 Mb
Release : 1967
Category : Mathematics
ISBN : UOM:39015078124834

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Elements of Mathematical Logic and Set Theory by Jerzy Słupecki,Ludwik Borkowski Pdf

Author : Harrie de Swart
Publisher : Springer
Page : 539 pages
File Size : 51,9 Mb
Release : 2018-11-28
Category : Philosophy
ISBN : 9783030032555

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Philosophical and Mathematical Logic by Harrie de Swart Pdf

This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

Author : Mordechai Ben-Ari
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781447103356

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Mathematical Logic for Computer Science by Mordechai Ben-Ari Pdf

This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.

Author : Ettore Casari
Publisher : Unknown
Page : 285 pages
File Size : 51,9 Mb
Release : 1969
Category : Mathematics
ISBN : 8870833380

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Aspects of mathematical logic by Ettore Casari Pdf

Author : H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 48,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475723557

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Mathematical Logic by H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas Pdf

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Author : Jerzy Słupecki,Ludwik Borkowski
Publisher : Pergamon
Page : 372 pages
File Size : 51,5 Mb
Release : 1967
Category : Mathematics
ISBN : UCAL:B4396227

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Elements of Mathematical Logic and Set Theory by Jerzy Słupecki,Ludwik Borkowski Pdf

Author : E. Casari
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 53,6 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9783642110801

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Aspects of Mathematical Logic by E. Casari Pdf

H. Hermes: Basic notions and applications of the theory of decidability.- D. Kurepa: On several continuum hypotheses.- A. Mostowski: Models of set theory.- A. Robinson: Problems and methods of model theory.- S. Sochor, B. Balcar: The general theory of semisets. Syntactic models of the set theory.

Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461572886

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Introduction to Mathematical Logic by Elliot Mendelsohn Pdf

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.

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 45,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213

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A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Author : Joseph R. Shoenfield
Publisher : CRC Press
Page : 281 pages
File Size : 40,7 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 9781351433303

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Mathematical Logic by Joseph R. Shoenfield Pdf

This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.

Author : J. Barwise
Publisher : Elsevier
Page : 1164 pages
File Size : 43,6 Mb
Release : 1982-03-01
Category : Computers
ISBN : 9780080933641

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Handbook of Mathematical Logic by J. Barwise Pdf

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Author : Richard E. Hodel
Publisher : Courier Corporation
Page : 514 pages
File Size : 47,6 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486497853

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An Introduction to Mathematical Logic by Richard E. Hodel Pdf

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.