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Mathematical Logic

Author: Ian Chiswell
Publisher: Oxford University Press on Demand
ISBN: 9780199215621
Size: 38.21 MB
Format: PDF, ePub
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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.

A First Course In Logic

Author: Shawn Hedman
Publisher: Oxford University Press on Demand
ISBN: 9780198529811
Size: 31.19 MB
Format: PDF
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"The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, thistext covers the fundamental topics in classical logic in a clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course."--BOOK JACKET.

Mathematical Logic

Author: Ian Chiswell
Publisher: OUP Oxford
ISBN: 9780198571001
Size: 52.77 MB
Format: PDF, Mobi
View: 6461
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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.

Modern Logic

Author: Graeme Forbes
Publisher: Oxford University Press, USA
ISBN: 9780195080292
Size: 13.76 MB
Format: PDF
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Modern Logic fills the strong need for a highly accessible, carefully structured introductory text in symbolic logic. The natural deduction system Forbes uses will be easy for students to understand, and the material is carefully structured, with graded exercises at the end of each section, selected answers to which are provided at the back of the book. The book's emphasis is on giving the student a thorough understanding of the concepts rather than just a facilitywith formal procedures.

Fundamentals Of Mathematical Logic

Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Size: 69.82 MB
Format: PDF, ePub
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This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Proof And Disproof In Formal Logic

Author: Richard Bornat
Publisher: Oxford University Press, USA
ISBN: 9780198530268
Size: 54.89 MB
Format: PDF, Docs
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Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, this text is a lively and entertaining introduction to formal logic and provides an excellent insight into how a simple logic works.

An Introduction To Formal Logic

Author: Peter Smith
Publisher: Cambridge University Press
ISBN: 9780521008044
Size: 19.94 MB
Format: PDF
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Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Propositional And Predicate Calculus A Model Of Argument

Author: Derek Goldrei
Publisher: Springer Science & Business Media
ISBN: 9781846282294
Size: 68.22 MB
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Designed specifically for guided independent study. Features a wealth of worked examples and exercises, many with full teaching solutions, that encourage active participation in the development of the material. It focuses on core material and provides a solid foundation for further study.

A Friendly Introduction To Mathematical Logic

Author: Christopher C. Leary
Publisher: Lulu.com
ISBN: 1942341075
Size: 43.67 MB
Format: PDF, ePub, Docs
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At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Godel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises."

Intermediate Logic

Author: David Bostock
Publisher: Clarendon Press
ISBN: 9780191567070
Size: 47.34 MB
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Intermediate Logic fills a serious gap in the range of university logic texts by offering a clear, reliable, general guide for students taking a second course in logic after completing a basic introduction. It will serve as an ideal follow-up to any of the standard introductory texts, and will give excellent preparation for advanced work in logical theory or applications of logic in philosophy, mathematics, or computing theory. - ;Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technological grounding. The author introduces and explains each concept and term, ensuring that readers have a firm foundation for study. He provides a broad, deep understanding of logic by adopting and comparing a variety of different methods and approaches. In the first section, Bostock covers such fundamental notions as truth, validity, entailment, quantification, and decision procedures. Part two lays out a definitive introduction to four key logical tools or procedures: semantic tableaux, axiomatic proofs, natural deduction, and sequent calculi. The final section opens up new areas of existence and identity, concluding by moving from orthodox logic to examination of `free logic'. Intermediate Logic provides an ideal secondary course in logic for university students, and a bridge to advanced study of such subjects as model theory, proof theory, and other specialized areas of mathematical logic. -