Methods And Applications Of Mathematical Logic
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Methods And Applications Of Mathematical Logic
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Author : Walter Alexandre Carnielli
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Methods And Applications Of Mathematical Logic written by Walter Alexandre Carnielli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Constitutes the proceedings of the Seventh Latin American Symposium on Mathematical Logic, held July 29-August 2, 1985, at the University of Campinas in Brazil. This book offers an introduction to the active lines of research in mathematical logic and emphasizes the connections to other fields - philosophy, computer science and probability theory.
Philosophical And Mathematical Logic
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Author : Harrie de Swart
language : en
Publisher: Springer
Release Date : 2018-11-28
Philosophical And Mathematical Logic written by Harrie de Swart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Philosophy categories.
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
Mathematical Logic
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Author : Wei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-26
Mathematical Logic written by Wei Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-26 with Mathematics categories.
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.
Introduction To Mathematical Logic
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Author : Elliot Mendelsohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Mathematical Logic written by Elliot Mendelsohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
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.
Mathematical Logic
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Author : H.-D. Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-11-15
Mathematical Logic written by H.-D. Ebbinghaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-15 with Mathematics categories.
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.
Mathematical Logic
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Author : George Tourlakis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Mathematical Logic written by George Tourlakis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.
Mathematical Logic In Asia
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Author : S. S. Goncharov
language : en
Publisher: World Scientific
Release Date : 2006
Mathematical Logic In Asia written by S. S. Goncharov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, o 1 -induction, completeness of Leoniewski''s systems, and reduction calculus for the satisfiability problem are also discussed. The coverage includes the answer to Kanovei''s question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories. Sample Chapter(s). Chapter 1: Another Characterization of the Deduction-Detachment Theorem (535 KB). Contents: Another Characterization of the Deduction-Detachment Theorem (S V Babyonyshev); On Behavior of 2-Formulas in Weakly o-Minimal Theories (B S Baizhanov & B Sh Kulpeshov); Arithmetic Turing Degrees and Categorical Theories of Computable Models (E Fokina); Negative Data in Learning Languages (S Jain & E Kinber); Effective Cardinals in the Nonstandard Universe (V Kanovei & M Reeken); Model-Theoretic Methods of Analysis of Computer Arithmetic (S P Kovalyov); The Functional Completeness of Leoniewski''s Systems (F Lepage); Hierarchies of Randomness Tests (J Reimann & F Stephan); Intransitive Linear Temporal Logic Based on Integer Numbers, Decidability, Admissible Logical Consecutions (V V Rybakov); The Logic of Prediction (E Vityaev); Conceptual Semantic Systems Theory and Applications (K E Wolff); Complexity Results on Minimal Unsatisfiable Formulas (X Zhao); and other papers. Readership: Researchers in mathematical logic and algebra, computer scientists in artificial intelligence and fuzzy logic."
Rethinking Logic Logic In Relation To Mathematics Evolution And Method
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Author : Carlo Cellucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-09
Rethinking Logic Logic In Relation To Mathematics Evolution And Method written by Carlo Cellucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-09 with Philosophy categories.
This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger
Mathematical Logic And Its Applications
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Author : Dimiter G. Skordev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Logic And Its Applications written by Dimiter G. Skordev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The Summer School and Conference on Mathematical Logic and its Applications, September 24 - October 4, 1986, Druzhba, Bulgaria, was honourably dedicated to the 80-th anniversary of Kurt Godel (1906 - 1978), one of the greatest scientists of this (and not only of this) century. The main topics of the Meeting were: Logic and the Foundation of Mathematics; Logic and Computer Science; Logic, Philosophy, and the Study of Language; Kurt Godel's life and deed. The scientific program comprised 5 kinds of activities, namely: a) a Godel Session with 3 invited lecturers b) a Summer School with 17 invited lecturers c) a Conference with 13 contributed talks d) Seminar talks (one invited and 12 with no preliminary selection) e) three discussions The present volume reflects an essential part of this program, namely 14 of the invited lectures and all of the contributed talks. Not presented in the volltme remai ned si x of the i nvi ted lecturers who di d not submi t texts: Yu. Ershov - The Language of!:-expressions and its Semantics; S. Goncharov - Mathematical Foundations of Semantic Programming; Y. Moschovakis - Foundations of the Theory of Algorithms; N. Nagornyj - Is Realizability of Propositional Formulae a GBdelean Property; N. Shanin - Some Approaches to Finitization of Mathematical Analysis; V. Uspensky - Algorithms and Randomness - joint with A.N.
Mathematical Logic
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Author : H.-D. Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Mathematical Logic written by H.-D. Ebbinghaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con sequence relation coincides with formal provability: By means of a calcu lus consisting of simple formal inference rules, one can obtain all conse quences of a given axiom system (and in particular, imitate all mathemat ical proofs). A short digression into model theory will help us to analyze the expres sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.