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  • © 2011

Treatise on Intuitionistic Type Theory

  • The author was a PhD student of Per Martin-Löf, the inventor of intuitionistic type theory, and has unique insights in the field.
  • There are many interesting connections between philosophy, logic, and computer science.
  • A new and pedagogical treatment of the double negation interpretation is included.

Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 22)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
  2. Prolegomena

    • Johan Georg Granström
    Pages 1-11
  3. Truth and Knowledge

    • Johan Georg Granström
    Pages 13-51
  4. The Notion of Set

    • Johan Georg Granström
    Pages 53-76
  5. Reference and Computation

    • Johan Georg Granström
    Pages 77-106
  6. Assumption and Substitution

    • Johan Georg Granström
    Pages 107-154
  7. Intuitionism

    • Johan Georg Granström
    Pages 155-173
  8. Back Matter

    Pages 175-196

About this book

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

Authors and Affiliations

  • Strängnäs, Sweden

    Johan Georg Granström

  • Uppsala, Sweden

    Johan Georg Granström

About the authors

Johan G. Granström (1977) holds an Uppsala doctorate in mathematical logic (2009). He had the privilege of having Em.Prof. Per Martin-Löf, the father of dependent types, as doctoral supervisor (2003-2009), along with Prof. Erik Palmgren, a renowned expert in constructive mathematics.

Dr. Granström has been a short-term research fellow at Ludwig-Maximilians-Universität München (2006-2007) and a research associate in formal methods for MDA at King’s College London (2009). Before entering into doctoral studies he was employed in the computer industry as systems developer, consultant, and software architect (1998-2003).  He worked as Systems and Solutions Architect at Svea Ekonomi (2009-2011) and is currently employed by Google, Zürich (2011- ).

Bibliographic Information

Buy it now

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access