Reasoning in Quantum Theory, 2004 Sharp and Unsharp Quantum Logics Trends in Logic Series, Vol. 22

"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking.
For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.

I Mathematical and Physical Background.- 1. The mathematical scenario of quantum theory and von Neumann’s axiomatization.- 2. Abstract axiomatic foundations of sharp QT.- 3. Back to Hilbert space.- 4. The emergence of fuzzy events in Hilbert space quantum theory.- 5. Effect algebras and quantum MV algebras.- 6. Abstract axiomatic foundations of unsharp quantum theory.- 7. To what extent is quantum ambiguity ambiguous?.- II Quantum Logics as Logic.- 8. Sharp quantum logics.- 9. Metalogical properties and anomalies of quantum logic.- 10. An axiomatization of OL and OQL.- 11. The metalogical intractability of orthomodularity.- 12. First-order quantum logics and quantum set theories.- 13. Partial classical logic, the Lindenbaum property and the hidden variable problem.- 14. Unsharp quantum logics.- 15. The Brouwer Zadeh logics.- 16. Partial quantum logics and ?ukasiewicz’ quantum logic.- 17. Quantum computational logic.- Conclusions.- Synoptic tables.- Index of Symbols.- Index of Names.

From the reviews:"The aim of the book is to present various logical investigations of quantum phenomena including ... quantum computation. ... The book is accomplished with a bibliography of 180 items. It is written in a very nice and fresh style ... . The authors are keeping the interest of the reader permanently on his trip through the book. ... The monograph is welcome in the quantum logic community, and it surely enriches the literature on quantum structures ... ." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1059 (10), 2005)"The book tries to delineate 'what we know of' quantum logics ... . The richness of the material of this book is impressive ... . this book is really important and deserves a place in any philosophical or technical library." (Décio Krause, Mathematical Reviews, Issue 2005 j)"This book is included as Volume 22 in the distinguished Book Series on 'Trends in Logic' published by Kluwer. ... The book is written for multidisciplinary audience. ... the presentation is human friendly, combining a simple introduction to essential mathematical concepts with a historical overview of their relevance to quantum theory. For anyone interested in quantum theory, this book is an essential reference." (George J. Klir, International Journal of General Systems, Vol. 34 (3), 2005)