"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.

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)

Autorentext

Maria Luisa Dalla Chiara, professor emeritus of Logic and Philosophy of Science at the University Florence is a past president of the "International Quantum Structures Association", of the "Italian Society of Logic and Philosophy of Science" and a past vice-president of the "Division of Logic, Methodology and Philosophy of Science". She is the author of books and articles concerning the following fields: quantum logic, quantum computation, foundations and philosophy of quantum theory, semantics of physical theories, theories of meaning, semantics of music. Roberto Giuntini, professor of Logic and Philosophy of Science at the University of Cagliari, is president of the "Italian Society of Logic and Philosophy of Science" and past president of the "International Quantum Structures Association". His research centers around the logico-algebraic structures of quantum theory and quantum computation. In 1998 he was awarded the Birkhoff-von Neumann Prize. Roberto Leporini received an MSc degree cum laude in Computer Science in 1999 and a PhD in Computer Science in 2004, both from the University of Milan. Since 2005 he is an assistant professor at the University of Bergamo. His main research interests are: quantum computing, quantum optics, quantum computational structures and logic. He has published over 40 papers in international journals and holds a patent on the construction of quantum circuits. He is the president of the "International Quantum Structures Association". Giuseppe Sergioli received an MSc degree in Theoretical Physics at the University of Catania and a PhD in Logic and Philosophy of Science at the University of Cagliari, where he is now an assistant professor. His main research interests are: quantum computing, quantum computational structures and quantum computational logics. He is the author of several papers published in prominent journals in the areas of physics, logic, foundations of physics and computer science.

Inhalt
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.