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| ian chiswell and wilfrid hodges mathematical logic: Mathematical Logic Roman Kossak, 2024-04-18 This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are usedto study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background. |
| ian chiswell and wilfrid hodges mathematical logic: Mathematical Logic Ian Chiswell, Wilfrid Hodges, 2007-05-17 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. |
| ian chiswell and wilfrid hodges mathematical logic: A First Course in Logic Shawn Hedman, 2004 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. |
| ian chiswell and wilfrid hodges mathematical logic: Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-08-21 Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
| ian chiswell and wilfrid hodges mathematical logic: Model Theory Wilfrid Hodges, 2008-06-19 Professor Hodges emphasizes definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference. |
| ian chiswell and wilfrid hodges mathematical logic: Logic Matters P. T. Geach, B. Geach, 1980-04-30 This is a significant and ofren rather demanding collection of essays. It is an anthology purring together the uncollected works of an important twentieth-century philosopher. Many of the articles treat one or another of the more important issues considered by analytic philosophers during the last quarter-century. Of significant importance to philosophers interested in researching the many topics contained in Logic Matters is the inclusion in this anthology of a rather extensive eight-page name-topic index.--Thomist The papers are arranged by topic: Historical Essays, Traditional Logic, Theory of Reference and Syntax, Intentionality, Quotation and Semantics, Set Theory, Identity Theory, Assertion, Imperatives and Practical Reasoning, Logic in Metaphysics and Theology. The broad range of issues that have engaged Geach's complex and systematic reasoning is impressive. In addition to classical logic, topics in ethics, ontology, and even the logic of religious dogmas are tackled .... the work in this collection is more brilliant and ingenious than it is difficult and demanding.--Philosophy of Science Geach displays his mastery of applying logical techniques and concepts to philosophical questions. Compared with most works in philosophical logic this book is remarkable for its range of topics. Plato, Aristotle, Aquinas, Russell, Wittgenstein, and Quine all figure prominently. Geach's style is remarkably lively considering the rightly argued matter. Although some of the articles treat rather technical questions in mathematical logic, most are accessible to philosophers with modest backgrounds in logic. --Choice |
| ian chiswell and wilfrid hodges mathematical logic: Logic Wilfrid Hodges, 1977 Logic is primarily about consistency - but not all types of consistency. For example if a man supports Arsenal one day and supports Spurs the next then he is fickle, but not necessarily illogical. The type of consistency which concerns logicians is not loyalty or justice or sincerity but compatibility of beliefs. Logic, therefore, involves studying the situations in which a sentence is true or valid and subsequently the rules which determine the validity or otherwise of a given argument. |
| ian chiswell and wilfrid hodges mathematical logic: Logic and Structure Dirk van Dalen, 2013-11-11 Logic appears in a 'sacred' and in a 'profane' form. The sacred form is dominant in proof theory, the profane form in model theory. The phenomenon is not unfamiliar, one observes this dichotomy also in other areas, e.g. set theory and recursion theory. For one reason or another, such as the discovery of the set theoretical paradoxes (Cantor, Russell), or the definability paradoxes (Richard, Berry), a subject is treated for some time with the utmost awe and diffidence. As a rule, however, sooner or later people start to treat the matter in a more free and easy way. Being raised in the 'sacred' tradition, I was greatly surprised (and some what shocked) when I observed Hartley Rogers teaching recursion theory to mathema ticians as if it were just an ordinary course in, say, linear algebra or algebraic topology. In the course of time I have come to accept his viewpoint as the didac tically sound one: before going into esoteric niceties one should develop a certain feeling for the subject and obtain a reasonable amount of plain working knowledge. For this reason I have adopted the profane attitude in this introductory text, reserving the more sacred approach for advanced courses. Readers who want to know more about the latter aspect of logic are referred to the immortal texts of Hilbert-Bernays or Kleene. |
| ian chiswell and wilfrid hodges mathematical logic: Mathematical Logic Ian Chiswell, Wilfrid Hodges, 2007-05-18 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. |
| ian chiswell and wilfrid hodges mathematical logic: Propositional and Predicate Calculus: A Model of Argument Derek Goldrei, 2005-12-27 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. |
| ian chiswell and wilfrid hodges mathematical logic: Lambda Calculus with Types Henk Barendregt, Wil Dekkers, Richard Statman, 2013-06-20 This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types. |
| ian chiswell and wilfrid hodges mathematical logic: Elements of Set Theory Herbert B. Enderton, 1977-04-28 This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning. |
| ian chiswell and wilfrid hodges mathematical logic: A Beginner's Guide to Mathematical Logic Raymond M. Smullyan, 2014-07-23 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 |
| ian chiswell and wilfrid hodges mathematical logic: A Concise Introduction to Mathematical Logic Wolfgang Rautenberg, 2010-07-01 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. |
| ian chiswell and wilfrid hodges mathematical logic: Beginning Model Theory Jane Bridge, 1977 |
| ian chiswell and wilfrid hodges mathematical logic: A Friendly Introduction to Mathematical Logic Christopher C. Leary, Lars Kristiansen, 2015 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 Gödel'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. |
| ian chiswell and wilfrid hodges mathematical logic: Upper Ten Thousand , 1920 |
| ian chiswell and wilfrid hodges mathematical logic: Elementary Differential Equations William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-08-14 With Wiley's Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including: Embedded & searchable equations, figures & tables Math XML Index with linked pages numbers for easy reference Redrawn full color figures to allow for easier identification Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two ] or three ] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
| ian chiswell and wilfrid hodges mathematical logic: Models and Ultraproducts A. B. Slomson, J. L. Bell, 2013-12-20 This first-year graduate text assumes only an acquaintance with set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic, and other topics. 1974 edition. |
| ian chiswell and wilfrid hodges mathematical logic: Dependenz und Valenz/ Dependency and Valency Vilmos Agel, Ludwig M. Eichinger, Hans Werner Eroms, Peter Hellwig, Hans Jurgen Heringer, Henning Lobin, 2003 Annotation The handbook provides an overview of the current status of this research. In its first volume, the handbook begins by presenting the historical background of the theories in which the conceptions are rooted and then goes on to deal with the individual ele. |
| ian chiswell and wilfrid hodges mathematical logic: FDA 1963 [protecting Consumers of Foods, Drugs, Cosmetics, and Household Chemicals]. United States. Food and Drug Administration, 1963 |
| ian chiswell and wilfrid hodges mathematical logic: Renewing U.S. Mathematics National Research Council, Division on Engineering and Physical Sciences, Commission on Physical Sciences, Mathematics, and Applications, Board on Mathematical Sciences, Committee on the Mathematical Sciences: Status and Future Directions, 1990-02-01 As requested by the National Science Foundation (NSF) and the Interagency Committee for Extramural Mathematics Programs (ICEMAP), this report updates the 1984 Report known as the David Report. Specifically, the charge directed the committee to (1) update that report, describing the infrastructure and support for U.S. mathematical sciences research; (2) assess trends and progress over the intervening five years against the recommendations of the 1984 Report; (3) briefly assess the field scientifically and identify significant opportunities for research, including cross-disciplinary collaboration; and (4) make appropriate recommendations designed to ensure that U.S. mathematical sciences research will meet national needs in coming years. Of the several components of the mathematical sciences community requiring action, its wellspring--university research departments--is the primary focus of this report. The progress and promise of research--described in the 1984 Report relative to theoretical development, new applications, and the refining and deepening of old applications--have if anything increased since 1984, making mathematics research ever more valuable to other sciences and technology. Although some progress has been made since 1984 in the support for mathematical sciences research, the goals set in the 1984 Report have not been achieved. Practically all of the increase in funding has gone into building the infractructure, which had deteriorated badly by 1984. While graduate and postdoctoral research, computer facilities, and new institutes have benefited from increased resources, some of these areas are still undersupported by the standards of other sciences. And in the area of research support for individual investigators, almost no progress has been made. A critical storage of qualified mathematical sciences researchers still looms, held at bay for the moment by a large influx of foreign researchers, an uncertain solution in the longer term. While government has responded substantially to the 1984 Report's recommendations, particularly in the support of infrastructure, the universities generally have not, so that the academic foundations of the mathematical sciences research enterprise are as shaky now as in 1984. The greatet progress has been made in the mathematics sciences community, whose members have shown a growing awareness of the problems confronting their discipline and increased interest in dealing with the problems, particularly in regard to communication with the public and government agencies and involvement in education. (AA) |
| ian chiswell and wilfrid hodges mathematical logic: The Arabic Language C. H. M. Versteegh, Kees Versteegh, 2014 An introductory guide for students of Arabic language, Arabic historical linguistics and Arabic sociolinguistics |
| ian chiswell and wilfrid hodges mathematical logic: Rationality, Control, and Freedom Curran F. Douglass, 2015-06-03 This book provides a concise, clear summary of the history of the free will vs. determinism controversy and offers a discussion of the basic differences of view. |
| ian chiswell and wilfrid hodges mathematical logic: An Introduction to Mathematical Logic Richard E. Hodel, 2013-01-01 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. |
| ian chiswell and wilfrid hodges mathematical logic: Opposing Europe?: The Comparative Party Politics of Euroscepticism Aleks Szczerbiak, Paul Taggart, 2008 This set provides a comprehensive review of Euroscepticism in contemporary European politics. Leading scholars address the strength and breadth of Euroscepticism across a range of EU member and candidate states, and draw out comparative lessons on the nature of political parties and party systems. |
| ian chiswell and wilfrid hodges mathematical logic: Building Models by Games Wilfrid Hodges, 2006-01-01 This volume introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. It covers basic model theory and examines a variety of algebraic applications, including completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras. Over 160 exercises. 1985 edition. |
| ian chiswell and wilfrid hodges mathematical logic: The Bulletin of Symbolic Logic , 2008 |
| ian chiswell and wilfrid hodges mathematical logic: Conceptions of Truth Kunne, 2003-06-05 Truth is one of the most debated topics in philosophy; Wolfgang Künne presents a comprehensive critical examination of all major theories. Conceptions of Truth is organized around a flow-chart comprising sixteen key questions, ranging from 'Is truth a property?' to 'Is truth epistemically constrained?' Künne expounds and engages with the ideas of many thinkers, from Aristotle and the Stoics, to Continental analytic philosophers like Bolzano, Brentano, andKotarbinski, to such leading figures in current debates as Dummett, Putnam, Wright, and Horwich. He explains many important distinctions (between varieties of correspondence, for example, between different conceptions of making true, between various kinds of eternalism and temporalism) which have so far been neglected in theliterature. Künne argues that it is possible to give a satisfactory 'modest' account of truth without invoking problematic notions like correspondence, fact, or meaning. And he offers a novel argument to support the realist claim that truth outruns justifiability.The clarity of exposition and the wealth of examples will make Conceptions of Truth an invaluable and stimulating guide for advanced students and scholars in metaphysics, epistemology and the philosophy of language. |
| ian chiswell and wilfrid hodges mathematical logic: Logics in AI Jan van Eijck, 1991-02-26 The European Workshop on Logics in Artificial Intelligence was held at the Centre for Mathematics and Computer Science in Amsterdam, September 10-14, 1990. This volume includes the 29 papers selected and presented at the workshop together with 7 invited papers. The main themes are: - Logic programming and automated theorem proving, - Computational semantics for natural language, - Applications of non-classical logics, - Partial and dynamic logics. |
| ian chiswell and wilfrid hodges mathematical logic: 数论导引 , 2007 本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。 |
| ian chiswell and wilfrid hodges mathematical logic: A Mathematical Introduction to Logic Herbert B. Enderton, 2001-01-23 A Mathematical Introduction to Logic |
| ian chiswell and wilfrid hodges mathematical logic: Mathematical Logic Joel W. Robbin, 2006-07-07 This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition. |
| ian chiswell and wilfrid hodges mathematical logic: An Introduction to Gödel's Theorems Peter Smith, 2007-07-26 Peter Smith examines Gödel's Theorems, how they were established and why they matter. |
| ian chiswell and wilfrid hodges mathematical logic: Vagueness and Contradiction Roy Sorensen, 2001-09-27 Did Buddha become a fat man in one second? Is there a tallest short giraffe? Epistemicists answer 'Yes!' They believe that any predicate that divides things divides them sharply. They solve the ancient sorites paradox by picturing vagueness as a kind of ignorance. The alternative solutions are radical. They either reject classical theorems or inference rules or reject our common sense view of what can exist. Epistemicists spare this central portion of our web of belief by challenging peripheral intuitions about the nature of language. So why is this continuation of the status quo so incredible? Why do epistemicists themselves have trouble believing their theory? In Vagueness and Contradiction Roy Sorensen traces our incredulity to linguistic norms that build upon our psychological tendencies to round off insignificant differences. These simplifying principles lead to massive inconsistency, rather like the rounding off errors of calculators with limited memory. English entitles speakers to believe each 'tolerance conditional' such as those of the form 'If n is small, then n + 1 is small.' The conjunction of these a priori beliefs entails absurd conditionals such as 'If 1 is small, then a billion is small.' Since the negation of this absurdity is an a priori truth, our a priori beliefs about small numbers are jointly inconsistent. One of the tolerance conditionals, at the threshold of smallness, must be an analytic falsehood that we are compelled to regard as a tautology. Since there are infinitely many analytic sorites arguments, Sorensen concludes that we are obliged to believe infinitely many contradictions. These contradictions are not specifically detectable. They are ineliminable, like the heat from a light bulb. Although the light bulb is not designed to produce heat, the heat is inevitably produced as a side-effect of illumination. Vagueness can be avoided by representational systems that make no concession to limits of perception, or memory, or testimony. But quick and rugged representational systems, such as natural languages, will trade 'rationality' for speed and flexibility. Roy Sorensen defends epistemicism in his own distinctive style, inventive and amusing. But he has some serious things to say about language and logic, about the way the world is and about our understanding of it. |
| ian chiswell and wilfrid hodges mathematical logic: Philosophy and Model Theory Tim Button, Sean P. Walsh, 2018 Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs. |
| ian chiswell and wilfrid hodges mathematical logic: Introduction to Logic Harry J. Gensler, 2012-08-06 Introduction to Logic combines likely the broadest scope of any logic textbook available with clear, concise writing and interesting examples and arguments. Its key features, all retained in the Second Edition, include: • simpler ways to test arguments than those available in competing textbooks, including the star test for syllogisms • a wide scope of materials, making it suitable for introductory logic courses (as the primary text) or intermediate classes (as the primary or supplementary book) • engaging and easy-to-understand examples and arguments, drawn from everyday life as well as from the great philosophers • a suitability for self-study and for preparation for standardized tests, like the LSAT • a reasonable price (a third of the cost of many competitors) • exercises that correspond to the LogiCola program, which may be downloaded for free from the web. This Second Edition also: • arranges chapters in a more useful way for students, starting with the easiest material and then gradually increasing in difficulty • provides an even broader scope with new chapters on the history of logic, deviant logic, and the philosophy of logic • expands the section on informal fallacies • includes a more exhaustive index and a new appendix on suggested further readings • updates the LogiCola instructional program, which is now more visually attractive as well as easier to download, install, update, and use. |
| ian chiswell and wilfrid hodges mathematical logic: Logic for Computer Science Jean H. Gallier, 2015-06-18 This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information. |
| ian chiswell and wilfrid hodges mathematical logic: American Book Publishing Record , 2007 |
| ian chiswell and wilfrid hodges mathematical logic: Dentists Mary Meinking, 2020-08 Open wide! Dentists care for people's teeth. Give readers the inside scoop on what it's like to be a dentist. Readers will learn what dentists do, the tools they use, and how people get this exciting job. |
Ian - Wikipedia
Ian or Iain is a name of Scottish Gaelic origin, which is derived from the Hebrew given name יוֹחָנָן (Yohanan, Yôḥānān) and corresponds to the English name John. The spelling Ian is an …
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Jan 21, 2022 · Anglicized form of Scottish Gaelic Iain, itself from Latin Iohannes (see John). It became popular in the United Kingdom outside of Scotland in the first half of the 20th century, …
Ian - Name Meaning and Origin
The name Ian is of Scottish origin and is derived from the Gaelic name "Iain," which is the Scottish form of John. It means "God is gracious" or "gift from God." Ian is a popular name in Scotland …
Ian - Baby name meaning, origin, and popularity | BabyCenter
Ian is the Scottish version of John, which derives from the Hebrew name Yochanan and means "God is gracious." Other versions of John that originate in the British Isles include Evan, Sean, Siobhan, …
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6 days ago · The name Ian is a boy's name of Scottish origin meaning "God is gracious". Ian is Scottish form of John, derived from the Hebrew name Yohanan. It is an Anglicization of the …
Ian - Wikipedia
Ian or Iain is a name of Scottish Gaelic origin, which is derived from the Hebrew given name יוֹחָנָן (Yohanan, Yôḥānān) and corresponds to the English name John. The spelling Ian is an …
Ian - YouTube
Welcome to Ian's OFFICIAL channel. Subscribe here for all music videos, audio releases, and official content from Ian.
Ian: Name Meaning, Origin, Popularity - Parents
6 days ago · Ian is of Scottish Gaelic origin and is the Scottish version of the name John. It comes from the Hebrew name Yohanan and means "God is gracious" or "the Lord is gracious." Ian …
Meaning, origin and history of the name Ian - Behind the Name
Jan 21, 2022 · Anglicized form of Scottish Gaelic Iain, itself from Latin Iohannes (see John). It became popular in the United Kingdom outside of Scotland in the first half of the 20th century, …
Ian - Name Meaning and Origin
The name Ian is of Scottish origin and is derived from the Gaelic name "Iain," which is the Scottish form of John. It means "God is gracious" or "gift from God." Ian is a popular name in Scotland …
Ian - Baby name meaning, origin, and popularity | BabyCenter
Ian is the Scottish version of John, which derives from the Hebrew name Yochanan and means "God is gracious." Other versions of John that originate in the British Isles include Evan, Sean, …
Ian: Name Meaning, Popularity and Info on BabyNames.com
Jun 11, 2025 · The name Ian is primarily a male name of Scottish origin that means God Is Gracious. Click through to find out more information about the name Ian on BabyNames.com.
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Feb 17, 2025 · Meaning: Ian means “God is gracious.” Gender: Ian is a boy’s name. Origin: Ian is the Gaelic variation of the name “John,” and comes from Hebrew. Pronunciation: You …
Ian - Baby Name Meaning, Origin, and Popularity for a Boy - Nameberry
6 days ago · The name Ian is a boy's name of Scottish origin meaning "God is gracious". Ian is Scottish form of John, derived from the Hebrew name Yohanan. It is an Anglicization of the …
