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  1. An introduction to fuzzy logic for practical applications.Kazuo Tanaka - 1996 - New York: Springer.
    Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge (...)
  2. Encyclopedia of the Scientific Revolution: From Copernicus to Newton.Wilbur Applebaum (ed.) - 2003 - Taylor & Francis US.
  3. Logic, Language, and Meaning, Volume 1: Introduction to Logic.L. T. F. Gamut - 1990 - Chicago, IL, USA: University of Chicago Press.
    Although the two volumes of _Logic, Language, and Meaning_ can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1, _Introduction to Logic_, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference and validity, (...)
  4. Models, Algebras, and Proofs.Xavier Caicedo & Carlos Montenegro - 1998 - CRC Press.
    "Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide.".
  5. The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
    This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
  6. Computability, an introduction to recursive function theory.Nigel Cutland - 1980 - New York: Cambridge University Press.
    What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland (...)
  7. What is a number?: mathematical concepts and their origins.Robert Tubbs - 2009 - Baltimore: Johns Hopkins University Press.
    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 topics (...)
  8. Mathematics and mind.Alexander George (ed.) - 1994 - New York: Oxford University Press.
    Those inquiring into the nature of mind have long been interested in the foundations of mathematics, and conversely this branch of knowledge is distinctive in that our access to it is purely through thought. A better understanding of mathematical thought should clarify the conceptual foundations of mathematics, and a deeper grasp of the latter should in turn illuminate the powers of mind through which mathematics is made available to us. The link between conceptions of mind and of mathematics has been (...)
  9. Plato's Philosophy of Mathematics.Anders Wedberg - 1955 - Greenwood Press.
  10. Logic and computation: interactive proof with Cambridge LCF.Lawrence C. Paulson - 1987 - New York: Cambridge University Press.
    Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, giving references (...)
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  11. Getting the Facts.Andrew King - 1998 - Copper Beach Books.
    Activities, projects, and games introduce the concepts of logic, probability, graphic analysis, and problem solving.
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  12. Logic and Philosophy: An Integrated Introduction.William H. Brenner - 1993 - Notre Dame, IN, USA: University of Notre Dame Press.
    In the Western philosophical tradition logical investigation and philosophical advance have been inextricably linked, each having stimulated and shaped the other. In Logic and Philosophy William H. Brenner examines a broad range of logical concepts and methods as they relate to the larger context of philosophical investigation and thus bring to light the philosophical depth of logic and its relevance to philosophy in general.
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  13. Non-standard logics for automated reasoning.Philippe Smets (ed.) - 1988 - San Diego: Academic Press.
    Although there are a few books available that give brief surveys of a variety of nonstandard logics, there is a growing need for a critical presentation providing both a greater depth and breadth of insight into these logics. This book assembles a wider and deeper view of the many potentially applicable logics. Three appendixes provide short tutorials on classical logic and modal logics, and give a brief introduction to the existing literature on the logical aspects of probability theory. These tutorials (...)
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  14. Set Theory, Logic and Their Limitations.Moshe Machover - 1996 - Cambridge University Press.
    This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations.
  15. Elements of Scientific Inquiry.Eric Martin & Daniel N. Osherson - 1998 - MIT Press.
    The authors present a theory of inductive logic that is built fromthe tools of logic and model theory.
  16. Mathematics, a Concise History and Philosophy.W. S. Anglin - 1994 - Springer.
    This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures (...)
  17. The Laboratory of the Mind: Thought Experiments in the Natural Sciences.James Robert Brown - 1991 - New York: Routledge.
    Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to defend (...)
  18. Trees: National Champions.Barbara Bosworth & Roger Conover - 2005 - MIT Press.
    Hauntingly beautiful photographs of 70 "champion" trees—each the biggest of its species—in a book that offers a dignified portrait of the American landscape and its true environmental heroes.
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  19. Philosophy of mathematics and mathematical practice in the seventeenth century.Paolo Mancosu (ed.) - 1996 - New York: Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...)
  20. Figures of thought: mathematics and mathematical texts.David Reed - 1995 - New York: Routledge.
    Figures of Thought looks at how mathematical works can be read as texts and examines their textual strategies. David Reed offers the first sustained and critical attempt to find a consistent argument or narrative thread in mathematical texts. Reed selects mathematicians from a range of historical periods and compares their approaches to organizing and arguing texts, using an extended commentary on Euclid's Elements as a central structuring framework. He develops fascinating interpretations of mathematicians' work throughout history, from Descartes to Hilbert, (...)
  21. Unbiased Stereology: Three-dimensional Measurement in Microscopy.Vyvyan Howard - 1998 - New York: Garland Science/Bios Scientific Publishers. Edited by M. G. Reed.
    The Advanced Methods series is intented for advanced undergraduates, postgraduates and established research scientists. Titles in the series are designed to cover current important areas of research in life sciences, and include both theoretical background and detailed protocols. The aim is to give researchers sufficient theory, supported by references, to take the given protocols and adapt them to their particular experimental systems. Unbiased Stereology , Second Edition expands the comprehensive practical first edition guide to 3-D measurements in microscopy using stereological (...)
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  22. Logic Programming: 20th International Conference, ICLP 2004, Saint-Malo, France, September 6-10, 2004, Proceedings.Bart Demoen & Vladimir Lifschitz - 2004 - Springer Verlag.
    This book constitutes the refereed proceedings of the 20th International Conference on Logic Programming, ICLP 2004, held in Saint-Malo, France in September 2004. The 28 revised full papers and 16 poster papers presented together with 2 invited papers were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on program analysis, constraints, alternative programming paradigms, answer set programming, and implementation.
  23. Deduction: Introductory Symbolic Logic.Daniel A. Bonevac - 2002 - Malden, MA: Wiley-Blackwell.
  24. Georg Cantor: His Mathematics and Philosophy of the Infinite.Joseph Warren Dauben - 1990 - Princeton University Press.
    One of the greatest revolutions in mathematics occurred when Georg Cantor promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula.Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's (...)
  25. Simplicial algorithms for minimizing polyhedral functions.M. R. Osborne - 2001 - New York: Cambridge University Press.
    Polyhedral functions provide a model for an important class of problems that includes both linear programming and applications in data analysis. General methods for minimizing such functions using the polyhedral geometry explicitly are developed. Such methods approach a minimum by moving from extreme point to extreme point along descending edges and are described generically as simplicial. The best-known member of this class is the simplex method of linear programming, but simplicial methods have found important applications in discrete approximation and statistics. (...)
  26. The Consistency of Arithmetic: And Other Essays.Storrs McCall - 2014 - Oxford and New York: Oxford University Press USA.
    This volume contains six new and fifteen previously published essays -- plus a new introduction -- by Storrs McCall. Some of the essays were written in collaboration with E. J. Lowe of Durham University. The essays discuss controversial topics in logic, action theory, determinism and indeterminism, and the nature of human choice and decision. Some construct a modern up-to-date version of Aristotle's bouleusis, practical deliberation. This process of practical deliberation is shown to be indeterministic but highly controlled and the antithesis (...)
  27. Frontiers of combining systems: third international workshop, FroCoS 2000, Nancy, France, March 22-24, 2000: proceedings.Helene Kirchner & Christophe Ringeissen (eds.) - 2000 - New York: Springer.
    This book constitutes the refereed proceedings of the Third International Workshop on Frontiers of Combining Systems, FroCoS 2000, held in Nancy, France, in March 2000.The 14 revised full papers presented together with four invited papers were carefully reviewed and selected from a total of 31 submissions. Among the topics covered are constraint processing, interval narrowing, rewriting systems, proof planning, sequent calculus, type systems, model checking, theorem proving, declarative programming, logic programming, and equational theories.
  28. Metalogic: an introduction to the metatheory of standard first order logic.Geoffrey Hunter - 1971 - Berkeley,: University of California Press.
    This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically ...
  29. Figures of Thought: Mathematics and Mathematical Texts.David Reed - 1994 - New York: Routledge.
    Rarely has the history or philosophy of mathematics been written about by mathematicians, and the analysis of mathematical texts themselves has been an area almost entirely unexplored. _Figures of Thought_ looks at ways in which mathematical works can be read as texts, examines their textual strategies and demonstrates that such readings provide a rich source of philosophical issues regarding mathematics: issues which traditional approaches to the history and philosophy of mathematics have neglected. David Reed, a professional mathematician himself, offers the (...)
  30. Figures of Thought: Mathematics and Mathematical Texts.David Reed - 1994 - New York: Routledge.
    Rarely has the history or philosophy of mathematics been written about by mathematicians, and the analysis of mathematical texts themselves has been an area almost entirely unexplored. _Figures of Thought_ looks at ways in which mathematical works can be read as texts, examines their textual strategies and demonstrates that such readings provide a rich source of philosophical issues regarding mathematics: issues which traditional approaches to the history and philosophy of mathematics have neglected. David Reed, a professional mathematician himself, offers the (...)
  31. Mathematics in a Postmodern Age: A Christian Perspective.Russell W. Howell & James Bradley - 2001 - Eerdmans Publishing Company.
    The discipline of mathematics has not been spared the sweeping critique of postmodernism. Is mathematical theory true for all time, or are mathematical constructs in fact fallible? This fascinating book examines the tensions that have arisen between modern and postmodern views of mathematics, explores alternative theories of mathematical truth, explains why the issues are important, and shows how a Christian perspective makes a difference. Contributors: W. James Bradley William Dembski Russell W. Howell Calvin Jongsma David Klanderman Christopher Menzel Glen VanBrummelen (...)
  32. Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap.Michael Potter - 2000 - Oxford and New York: Oxford University Press.
    This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.
  33. Symbolic logic and mechanical theorem proving.Chin-Liang Chang - 1973 - San Diego: Academic Press. Edited by Richard Char-Tung Lee.
    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.
  34. Computer Science Logic: 6th Workshop, Csl'92, San Miniato, Italy, September 28 - October 2, 1992. Selected Papers.Egon Börger, Gerhard Jäger, Hans Kleine Büning, Simone Martini & Michael M. Richter - 1993 - Springer Verlag.
    This workshop on stochastic theory and adaptive control assembled many of the leading researchers on stochastic control and stochastic adaptive control to increase scientific exchange and cooperative research between these two subfields of stochastic analysis. The papers included in the proceedings include survey and research. They describe both theoretical results and applications of adaptive control. There are theoretical results in identification, filtering, control, adaptive control and various other related topics. Some applications to manufacturing systems, queues, networks, medicine and other topics (...)
  35. Computer Science Logic.Dirk van Dalen & Marc Bezem (eds.) - 1997 - Springer.
    The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields. The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The (...)
  36. Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
    On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.
  37. New Directions in the Philosophy of Mathematics: An Anthology.Thomas Tymoczko (ed.) - 1998 - Princeton University Press.
    This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
  38. An accompaniment to higher mathematics.George R. Exner - 1997 - New York: Springer.
    This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, (...)
  39. Converging Realities: Toward a Common Philosophy of Physics and Mathematics.Roland Omnès - 2004 - Princeton University Press.
    The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject.
  40. Mathematics, science, and epistemology.Imre Lakatos, Gregory Currie & John Worrall - 1978 - New York: Cambridge University Press.
  41. Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
  42. The combinatory programme.Erwin Engeler (ed.) - 1994 - Boston: Birkhäuser.
    Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 to (...)
  43. Mathematics, science, and epistemology.Imre Lakatos - 1978 - New York: Cambridge University Press. Edited by Gregory Currie & John Worrall.
    Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.
  44. Proof theory: a selection of papers from the Leeds Proof Theory Programme, 1990.Peter Aczel, Harold Simmons & Stanley S. Wainer (eds.) - 1992 - New York: Cambridge University Press.
    This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.
  45. But why does it work?: mathematical argument in the elementary classroom.Susan Jo Russell (ed.) - 2017 - Portsmouth, NH: Heinemann.
    Mathematical argument in the elementary grades : what and why? -- Elementary students as mathematicians -- The teaching model -- Using the lesson sequences : what the teacher does -- Mathematical argument in the elementary classroom : impact on students and teachers.
  46. Uncertain Inference.Henry E. Kyburg Jr & Choh Man Teng - 2001 - Cambridge University Press.
    Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book (...)
  47. How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics.William Byers - 2010 - Princeton University Press.
    "--David Ruelle, author of "Chance and Chaos" "This is an important book, one that should cause an epoch-making change in the way we think about mathematics.
  48. A transfinite type theory with type variables.P. B. Andrews - 1965 - Amsterdam,: North-Holland Pub. Co..
  49. Extensions of Logic Programming: 5th International Workshop, Elp '96, Leipzig, Germany, March 28 - 30, 1996. Proceedings.Roy Dyckhoff, Heinrich Herre & Peter Schroeder-Heister - 1996 - Springer.
    This book constitutes the refereed proceedings of the 5th International Workshop on Extensions of Logic Programming, ELP '96, held in Leipzig, Germany in March 1996. The 18 full papers included were carefully selected by the program committee and are presented together with three invited papers. Among the topics addressed in this book are categorical logic programming, correctness of logic programs, functional-logic languages, implementation issues, linear logic programming, nonmonotonic reasoning, and proof search.
  50. Symbolic Logic.Dale Jacquette - 2001 - Wadsworth Publishing Company.
    This comprehensive intro text covers central topics of elementary and symbolic logic. It contains many problems and exercises and provides a solid foundation for continued study of advanced topics in logic.
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