Reasoning in Quantum Theory

Sharp and Unsharp Quantum Logics

Maria Luisa Dalla Chiara, Roberto Giuntini, Richard Greechie (Autoren)

Buch | Hardcover

298 Seiten

2004
Springer-Verlag New York Inc.
978-1-4020-1978-4 (ISBN)

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"Is quantum logic really logic?" The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking. from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation.

"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.

Erscheint lt. Verlag	31.3.2004
Reihe/Serie	Trends in Logic ; 22
Zusatzinfo	XXII, 298 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	210 x 279 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	1-4020-1978-5 / 1402019785
ISBN-13	978-1-4020-1978-4 / 9781402019784
Zustand	Neuware