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Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics
  • Language: en
  • Pages: 432

Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics

This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked...

Lectures on Rings and Modules
  • Language: en
  • Pages: 196

Lectures on Rings and Modules

This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of hi...

Introduction to Higher-Order Categorical Logic
  • Language: en
  • Pages: 308

Introduction to Higher-Order Categorical Logic

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

From Word to Sentence
  • Language: en
  • Pages: 154

From Word to Sentence

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Handbook of Philosophical Logic
  • Language: en
  • Pages: 382

Handbook of Philosophical Logic

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications

Completions of Categories
  • Language: en
  • Pages: 76

Completions of Categories

  • Type: Book
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  • Published: 2006-11-14
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  • Publisher: Springer

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Logic, Methodology and Philosophy of Science IX
  • Language: en
  • Pages: 1006

Logic, Methodology and Philosophy of Science IX

  • Type: Book
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  • Published: 1994
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  • Publisher: Elsevier

This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.

Sketches of an Elephant: A Topos Theory Compendium
  • Language: en
  • Pages: 836

Sketches of an Elephant: A Topos Theory Compendium

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.

Horizons of the Mind. A Tribute to Prakash Panangaden
  • Language: en
  • Pages: 514

Horizons of the Mind. A Tribute to Prakash Panangaden

  • Type: Book
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  • Published: 2014-05-23
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  • Publisher: Springer

This Festschrift volume contains papers presented at a conference, Prakash Fest, held in honor of Prakash Panangaden, in Oxford, UK, in May 2014, to celebrate his 60th birthday. Prakash Panangaden has worked on a large variety of topics including probabilistic and concurrent computation, logics and duality and quantum information and computation. Despite the enormous breadth of his research, he has made significant and deep contributions. For example, he introduced logic and a real-valued interpretation of the logic to capture equivalence of probabilistic processes quantitatively. The 25 papers included in this volume were carefully reviewed. They cover a large variety of topics in theoretical computer science.

Logic from Russell to Church
  • Language: en
  • Pages: 1069

Logic from Russell to Church

  • Type: Book
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  • Published: 2009-06-16
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  • Publisher: Elsevier

This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights