Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The proof-theoretical system represents a simpler and more illuminating method than alternative approaches, and this volume offers a succinct, coherent illustration of its applications to natural deduction. 1965 edition.
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3 of 3 people found the following review helpful:
3.0 out of 5 stars
Dag Prawitz' 1965 Ph.D. thesis,
By Scott (Dubuque, IA) - See all my reviews
This review is from: Natural Deduction: A Proof-Theoretical Study (Dover Books on Mathematics) (Paperback)
This nice little Dover 2006 reprint of the 1965 Ph.D. thesis at the University of Stockholm by Dag Prawitz contains 7 short chapters and 3 appendices. They are: I. Natural Dedution of Gentzen Type / II. The Inversion Principle / III. Normal Deductions in Classical Logic / IV. Normal Deductions in Intuitionistic Logic / V. Second-Order Logic / VI. Modal Logic / VII. Some Other Concepts of Implication / APPENDIX A. The Calculi of Sequents / APPENDIX B. On a Set Theory by Fitch / APPENDIX C. Notes on Some Other Variants of Natural DeductionPrawitz wrote a highly informative new preface for the Dover reissuance of his thesis monograph. This book is not highly difficult, but it ultimately had to satisfy Prawitz' Stockholm Ph.D. committee so he tended to lay out the fundamentals of the logics he wrote about, without showing any 'operations' of those logics. For me that isn't a very satisfying read. Plus, I didn't feel a need to go at logic for several philosophical positions as Prawitz did. All this makes clear that this book is nothing like a regular logic textbook and shouldn't be mistaken as such. I read only the first two chapters last winter. In some circles this thesis is still regarded highly as groundbreaking in most of its subjects, so for $10 it's a steal. If you are interested in proof theoretical logic, buy this little book. Personally I'm not much proof theoretical at all, but this is still a fine reference for me, if only because the main introduction and elimination rules are clearly shown in Chapter I. Here is a much more difficult proof theory book I own that is an actual textbook: Basic Proof Theory (Cambridge Tracts in Theoretical Computer Science) and a phenomenal logic textbook I fully read in Nov11, and my absolute favorite book! Logic for Computer Scientists (Modern Birkhäuser Classics)
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