propositional and predicate calculus a model of argument

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Propositional And Predicate Calculus A Model Of Argument

Author : Derek Goldrei
ISBN : 1846282292
Genre : Mathematics
File Size : 58. 53 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.

Propositional And Predicate Calculus A Model Of Argument

Author : Derek Goldrei
ISBN : 1852339217
Genre : Mathematics
File Size : 31. 79 MB
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At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique book covers two entirely different ways of looking at such reasoning. Topics include: the representation of mathematical statements by formulas in a formal language; logical consequence of one formula from others; the compactness theorem and an introduction to model theory; and more.

Propositional And Predicate Calculus A Model Of Argument

Author : Derek Goldrei
ISBN : 1848008260
Genre : Mathematics
File Size : 79. 49 MB
Format : PDF
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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.

Mathematical Logic Part 1

Author : René Cori
ISBN : 9780191589775
Genre : Mathematics
File Size : 50. 50 MB
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Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science. This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic.

An Introduction To Formal Logic

Author : Peter Smith
ISBN : 0521008042
Genre : Mathematics
File Size : 23. 4 MB
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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.

Beginning Logic

Author : E.J. Lemmon
ISBN : 0412380900
Genre : Mathematics
File Size : 33. 27 MB
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The aim of this book is to provide an exposition of elementary formal logic. The course, which is primarily intended for first-year students who have no previous knowledge of the subject, forms a working basis for more advanced reading and is presented in such a way as to be intelligible to the layman. The nature of logic is examined with the gradual introduction of worked samples showing how to distinguish the sound statement from the unsound. Arguments whose soundness cannot be proved by propositional calculus are discussed, and it is shown how formalization can reveal the logical form of arguments. The final section of the book deals with the application of the predicate calculus as applied in various other fields of logic.

First Order Modal Logic

Author : M. Fitting
ISBN : 9789401152921
Genre : Philosophy
File Size : 65. 82 MB
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This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Mathematical Logic

Author : Ian Chiswell
ISBN : 9780198571001
Genre : Mathematics
File Size : 54. 64 MB
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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 becalculated; 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, assumingMatiyasevich'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 andcomputer 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.

Intermediate Logic

Author : David Bostock
ISBN : 0191567078
Genre : Mathematics
File Size : 77. 59 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. -

Classic Set Theory

Author : D.C. Goldrei
ISBN : 9781351460606
Genre : Mathematics
File Size : 81. 10 MB
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Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

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