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#### Adapting Proofs-as-Programs

Springer New York 2007; US$ 169.00This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was ?rst conceived. At that time, there was a belief that proofs-as-programs had the - tential for practical application to semi-automated... more...

#### Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Springer Berlin Heidelberg 2008; US$ 109.00This 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 Opposition

Springer 2012; US$ 89.95aiThe 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...

#### A Framework for Priority Arguments

Cambridge University Press 2010; US$ 76.00This book presents a unifying framework for using priority arguments to prove theorems in computability. more...

#### Frege's Notations

Palgrave Macmillan 2012; US$ 95.00A 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 Theory

Elsevier Science 1998; US$ 235.00This 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 Reasoning

Cambridge University Press 1997; US$ 52.00The purpose of this book is to introduce the basic ideas of mathematical proof and reasoning to students starting university mathematics. more...

#### Learning to Reason

Wiley 2011; US$ 186.00Learn 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 Isomorphism

Elsevier Science 2006; US$ 170.00The 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...

#### Le?niewski's Systems of Logic and Foundations of Mathematics

Springer International Publishing 2013; US$ 129.00Offering an expansive critical commentary, this meticulous assessment of the ground-breaking work of the philosopher Stanislaw Le?niewski focuses exclusively on primary texts and explores the full range of work by a master logician of the Lvov-Warsaw school. more...