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Proof theory

  • Adapting Proofs-as-Programsby Iman Hafiz Poernomo; Martin Wirsing; John Newsome Crossley

    Springer 2007; US$ 139.00

    Details developments in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems. more...

  • Applied Proof Theoryby Ulrich Kohlenbach

    Springer 2008; US$ 99.00

    This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as - via extended case studies - carrying out some of these... more...

  • Around and Beyond the Square of Oppositionby Jean-Yves Béziau; Dale Jacquette

    Springer 2012; US$ 89.95

    aiThe theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, psychology. The square can also be generalized in other two-dimensional or multi-dimensional... more...

  • Frege's Notationsby Gregory Landini; Michael Beaney

    Palgrave Macmillan 2012; US$ 90.00

    A new approach to reading Frege's notations that adheres to the modern view that terms and well-formed formulas are any disjoint syntactic categories. On this new approach, we can at last read Frege's notations in their original form revealing striking new solutions to many of the outstanding problems of interpreting his philosophy. more...

  • Handbook of Proof Theoryby S.R. Buss

    Elsevier Science 1998; US$ 235.00

    This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics... more...

  • An Introduction to Mathematical Reasoningby Peter J. Eccles

    Cambridge University Press 1997; US$ 47.00

    The purpose of this book is to introduce the basic ideas of mathematical proof and reasoning to students starting university mathematics. more...

  • Learning to Reasonby Nancy Rodgers

    Wiley 2011; US$ 180.00

    Learn how to develop your reasoning skills and how to write well-reasoned proofs Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques... more...

  • Lectures on the Curry-Howard Isomorphismby Morten Heine Sørensen; Pawel Urzyczyn

    Elsevier Science 2006; US$ 165.00

    The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic... more...

  • Lesniewski's Systems of Logic and Foundations of Mathematicsby Rafal Urbaniak

    Springer 2013; US$ 129.00

    This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw  Lesniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The authorâ??s nuanced survey eschews secondary commentary, analyzing Lesniewski's core philosophical views and evaluating... more...

  • Linear Logic in Computer Scienceby Thomas Ehrhard; Jean-Yves Girard; Paul Ruet; Philip Scott

    Cambridge University Press 2004; US$ 109.00

    This book illustrates linear logic in the application of proof theory to computer science. more...