Search results for 'Logic, Symbolic and mathematical Study and teaching' (try it on Scholar)

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  1. Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.) (2009). Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge.score: 822.0
    Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help ...
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  2. Zoltan P. Dienes (1966). Learning Logic, Logical Games. [New York]Herder and Herder.score: 807.0
     
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  3. Maurice Joseph Burke (ed.) (2008). Navigating Through Reasoning and Proof in Grades 9-12. National Council of Teachers of Mathematics.score: 762.0
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  4. Xinli Wang (2009). Symbolic Logic Study Guide. University Readers.score: 612.0
    The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve sample (...)
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  5. Ian Chiswell (2007). Mathematical Logic. Oxford University Press.score: 525.6
    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 (...)
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  6. Stephen Cole Kleene (1967/2002). Mathematical Logic. Dover Publications.score: 505.6
    Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part (...)
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  7. G. T. Kneebone (1963/2001). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover.score: 505.6
    Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.
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  8. Graeme Forbes (1994). Modern Logic: A Text in Elementary Symbolic Logic. Oxford University Press.score: 505.6
    Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a special appendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, (...)
     
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  9. Heinz-Dieter Ebbinghaus (1996). Mathematical Logic. Springer.score: 477.6
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The (...)
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  10. M. Ben-Ari (1993/2003). Mathematical Logic for Computer Science. Prentice Hall.score: 477.6
    Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but 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. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.The logical systems presented are:- Propositional calculus (including binary decision diagrams);- Predicate calculus;- Resolution;- Hoare logic;- (...)
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  11. J. L. Bell (1977). A Course in Mathematical Logic. Sole Distributors for the U.S.A. And Canada American Elsevier Pub. Co..score: 477.6
    A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.
     
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  12. Herbert B. Enderton (1972). A Mathematical Introduction to Logic. New York,Academic Press.score: 408.0
    A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, (...)
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  13. J. P. Cleave (1991). A Study of Logics. Oxford University Press.score: 405.6
    It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to name but a few - which have originated in the areas of mathematical logic and computer science. In this book the author presents a systematic study of this rich harvest of logics via Tarski's well-known axiomatization of the notion of logical consequence. New and sometimes unorthodox treatments are given (...)
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  14. Robert Tubbs (2009). What is a Number?: Mathematical Concepts and Their Origins. Johns Hopkins University Press.score: 397.6
    Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of (...)
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  15. Ann M. Singleterry (1967). Review: Patrick Suppes, Mathematical Logic for the Schools; Patrick Suppes, Frederick Binford, Experimental Teaching of Mathematical Logic in the Elementary School. [REVIEW] Journal of Symbolic Logic 32 (3):422-422.score: 372.0
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  16. Stewart Shapiro (ed.) (2005). The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press.score: 370.4
    Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these (...)
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  17. Aleksy Mołczanow (2012). Quantification: Transcending Beyond Frege's Boundaries: A Case Study in Transcendental-Metaphysical Logic. Brill.score: 369.6
    Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely ...
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  18. Jean-Yves Béziau (ed.) (2005). Logica Universalis: Towards a General Theory of Logic. Birkhäuser.score: 369.6
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the (...)
     
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  19. Stanisław J. Surma (ed.) (1973). Studies in the History of Mathematical Logic. Wrocław,Zakład Narodowy Im. Ossolinskich.score: 368.0
  20. Walter Carnielli (1986). Seventh Latin American on Mathematical Logic- Meeting of the Association for Symbolic Logic: Campinas, Brazil, 1985. Journal of Symbolic Logic 51 (4):1093-1103.score: 360.0
    This publication refers to the proceedings of the Seventh Latin American on Mathematical Logic held in Campinas, SP, Brazil, from July 29 to August 2, 1985. The event, dedicated to the memory of Ayda I. Arruda, was sponsored as an official Meeting of the Association for Symbolic Logic. Walter Carnielli. -/- The Journal of Symbolic Logic Vol. 51, No. 4 (Dec., 1986), pp. 1093-1103.
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  21. Michał Walicki (2012). Introduction to Mathematical Logic. World Scientific.score: 358.2
    A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics (...)
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  22. S. B. Cooper & J. K. Truss (eds.) (1999). Models and Computability: Invited Papers From Logic Colloquium '97, European Meeting of the Association for Symbolic Logic, Leeds, July 1997. Cambridge University Press.score: 358.2
    Together, Models and Computability and its sister volume Sets and Proofs will provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic). It is expected that the breadth and timeliness of these two volumes will prove an invaluable and unique resource for specialists, post-graduate researchers, and the (...)
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  23. S. W. P. Steen (1972). Mathematical Logic with Special Reference to the Natural Numbers. Cambridge [Eng.]University Press.score: 358.2
    This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in (...)
     
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  24. Andrea Cantini (1996). Logical Frameworks for Truth and Abstraction: An Axiomatic Study. Elsevier Science B.V..score: 345.6
    This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these (...)
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  25. Gerard Allwein & Jon Barwise (eds.) (1996). Logical Reasoning with Diagrams. Oxford University Press.score: 336.4
    One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore (...)
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  26. José Ferreirós (2010). La lógica matemática: una disciplina en busca de encuadre (Mathematical Logic). Theoria 25 (3):279-299.score: 336.0
    RESUMEN: Se ofrece un análisis de las transformaciones disciplinares que ha experimentado la lógica matemática o simbólica desde su surgimiento a fines del siglo XIX. Examinaremos sus orígenes como un híbrido de filosofía y matemáticas, su madurez e institucionalización bajo la rúbrica de “lógica y fundamentos”, una segunda ola de institucionalización durante la Posguerra, y los desarrollos institucionales desde 1975 en conexión con las ciencias de la computación y con el estudio de lenguaje e informática. Aunque se comenta algo de (...)
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  27. J. Y. Beziau (ed.) (2005). Logica Universalis. Birkhäuser Verlog.score: 333.6
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the (...)
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  28. Volker Peckhaus (1999). 19th Century Logic Between Philosophy and Mathematics. Bulletin of Symbolic Logic 5 (4):433-450.score: 333.0
    The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of (...)
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  29. Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press.score: 329.6
    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, this text covers the fundamental topics in classical logic in an extremely 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, (...)
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  30. George J. Tourlakis (2003). Lectures in Logic and Set Theory. Cambridge University Press.score: 329.6
    This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques (...)
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  31. Rudolf Carnap (1958). Introduction to Symbolic Logic and its Applications. New York, Dover Publications.score: 328.2
    Clear, comprehensive, intermediate introduction to logical languages, applications of symbolic logic to physics, mathematics, biology.
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  32. Costas Dimitracopoulos (ed.) (2008). Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28-August 3, 2005. [REVIEW] Cambridge University Press.score: 328.2
    The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments. Highlights of this volume from the 2005 meeting include three papers on different aspects of connections between model theory and algebra; a survey of recent major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of (...)
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  33. Imre Lakatos (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.score: 324.0
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or (...)
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  34. Robert Feys (1969). Dictionary of Symbols of Mathematical Logic. Amsterdam, North-Holland Pub. Co..score: 322.2
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  35. A. C. Leisenring (1969). Mathematical Logic and Hilbert's & Symbol. London, Macdonald Technical & Scientific.score: 322.2
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  36. Johanna N. Y. Franklin (forthcoming). Reviewed Work(S): Lowness Properties and Randomness. Advances in Mathematics, Vol. 197 by André Nies; Lowness for the Class of Schnorr Random Reals. SIAM Journal on Computing, Vol. 35 by Bjørn Kjos-Hanssen; André Nies; Frank Stephan; Lowness for Kurtz Randomness. The Journal of Symbolic Logic, Vol. 74 by Noam Greenberg; Joseph S. Miller; Randomness and Lowness Notions Via Open Covers. Annals of Pure and Applied Logic, Vol. 163 by Laurent Bienvenu; Joseph S. Miller; Relativizations of Randomness and Genericity Notions. The Bulletin of the London Mathematical Society, Vol. 43 by Johanna N. Y. Franklin; Frank Stephan; Liang Yu; Randomness Notions and Partial Relativization. Israel Journal of Mathematics, Vol. 191 by George Barmpalias; Joseph S. Miller; André Nies. [REVIEW] Association for Symbolic Logic: The Bulletin of Symbolic Logic.score: 315.0
    Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.
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  37. Patrick Suppes (1964/2002). First Course in Mathematical Logic. Dover Publications.score: 314.4
    This introduction to rigorous mathematical logic is simple enough in both presentation and context for students of a wide range of ages and abilities. Starting with symbolizing sentences and sentential connectives, it proceeds to the rules of logical inference and sentential derivation, examines the concepts of truth and validity, and presents a series of truth tables. Subsequent topics include terms, predicates, and universal quantifiers; universal specification and laws of identity; axioms for addition; and universal generalization. Throughout the book, the (...)
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  38. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.score: 313.2
    This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation (...)
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  39. W. V. Quine (1951). Mathematical Logic. Cambridge, Harvard University Press.score: 313.2
    INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...
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  40. Hao Wang (1981/1993). Popular Lectures on Mathematical Logic. Dover Publications.score: 313.2
    Noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. After historical survey, lucid treatment of set theory, model theory, recursion theory and constructivism and proof theory. Place of problems in development of theories of logic, logic’s relationship to computer science, more. Suitable for readers at many levels of mathematical sophistication. 3 appendixes. Bibliography. 1981 edition.
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  41. David Hilbert (1950/1999). Principles of Mathematical Logic. Ams Chelsea.score: 313.2
    Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.
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  42. A. Prestel (2011). Mathematical Logic and Model Theory: A Brief Introduction. Springer.score: 313.2
    Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...
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  43. John N. Crossley (ed.) (1972/1990). What is Mathematical Logic? Dover Publications.score: 313.2
    This lively introduction to mathematical logic, easily accessible to non-mathematicians, offers an historical survey, coverage of predicate calculus, model theory, Godel’s theorems, computability and recursivefunctions, consistency and independence in axiomatic set theory, and much more. Suggestions for Further Reading. Diagrams.
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  44. John Venn (1894/1971). Symbolic Logic. New York,B. Franklin.score: 313.2
    SYMBOLIC LOGIC. CHAPTER I. ON THE FORMS OF LOGICAL PROPOSITION. IT has been mentioned in the Introduction that the System of Logic which this work is ...
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  45. Wolfgang Rautenberg (2006). A Concise Introduction to Mathematical Logic. Springer.score: 313.2
    Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that (...)
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  46. Susanne Katherina Knauth Langer (1967). An Introduction to Symbolic Logic. New York, Dover Publications.score: 313.2
    Famous classic has introduced hundreds of thousands to symbolic logic, via clear, thorough, precise exposition.
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  47. Alessandro Andretta, Keith Kearnes & Domenico Zambella (eds.) (2008). Logic Colloquium 2004: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Torino, Italy, July 25-31, 2004. [REVIEW] Cambridge University Press.score: 313.2
    Highlights of this volume from the 2004 Annual European Meeting of the Association for Symbolic Logic (ASL) include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect "abstract elementary classes" to issues around p-adic integration.
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  48. Walter A. Carnielli & Luiz Carlos P. D. Pereira (eds.) (1995). Logic, Sets and Information: Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Centro de Lógica, Epistemologia e História da Ciência, Unicamp.score: 313.2
    Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Coleção CLE, volume 14, 1995. Centro De Lógica, Epistemologia e História da Ciência, Unicamp, Campinas, SP, Brazil.
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  49. Chin-Liang Chang (1973/1987). Symbolic Logic and Mechanical Theorem Proving. Academic Press.score: 313.2
    This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
     
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  50. Joel W. Robbin (1969/2006). Mathematical Logic: A First Course. Dover Publications.score: 313.2
    Suitable for advanced undergraduates and graduate students from diverse fields and varying backgrounds, this self-contained course in mathematical logic features numerous exercises that vary in difficulty. The author is a Professor of Mathematics at the University of Wisconsin.
     
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