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Current issues in quantum logic. (Proceedings of the Workshop on Quantum Logic held in Erice, Sicily, December 2-9, 1979). (English) Zbl 0537.03044

Ettore Majorana International Science Series (Physical Sciences), Vol. 8. New York - London: Plenum Press. IX, 492 p. $ 59.50 (1981).
The history of quantum logic begins with Birkhoff and von Neumann, who, in 1936, published the algebraic foundations of quantum mechanics. The contributors of this volume approach the subject from many different points of view and with different backgrounds, thus the collection shows a great vitality of research in the area of quantum logic. This material represents an up-to-date and virtually complete source of information on the study of the field.
The contributions are grouped into six chapters: I. Classification of different areas of quantum logic, and open problems, II. Comparison and unification of different approaches to quantum theories; problems of interpretation, III. Formal quantum logic; axiomatics, IV. Modal interpretations of quantum logic, V. Quantum set theory, VI. Advances concerning mathematical structure; other problems.
Contents: P. Mittelstaedt: Classification of different areas of work afferent to quantum logic (pp. 3-16); Bas C. van Fraassen: Assumptions and interpretations of quantum logic (pp. 17-31); D. Foulis and C. Randall: What are quantum logics and what ought they to be? (pp. 35-52); G. Hardegree and P. Frazer: Charting the labyrinth of quantum logics: a progress report (pp. 53-76); R. I. G. Hughes: Realism and quantum logic (pp. 77-87); J. Bub: What does quantum logic explain? (pp. 89-100); R. Cooke and J. Hilgevoord: A new approach to equivalence in quantum logic (pp. 101- 113); J. Dorling: How to rewrite a stochastic dynamical theory so as to generate a measurement paradox (pp. 115-118); M. Abbati and A. Manià: The quantum logical and the operational description for physical systems (pp. 119-127); J. Czelakowski: Partial referential matrices for quantum logics (pp. 131-146); M. Dalla Chiara: Some metalogical pathologies of quantum logic (pp. 147-159); S. Bernini: Quantum logic as an extension of classical logic (pp. 161-171); E. Stachow: Sequential quantum logic (pp. 173-191); A. Kron, Z. Maric, and S. Vujosevic: Entailment and quantum logic (pp. 193- 207); G. Hardegree: Some problems and methods in formal quantum logic (pp. 209-225); Bas C. Van Fraassen: A modal interpretation of quantum mechanics (pp. 229-258); P. Mittelstaedt: The dialogic approach to modalities in the language of quantum physics (pp. 259-281); S. Bugajski: The inner language of operational quantum mechanics (pp. 283-299); G. Takeuti: Quantum set theory (pp. 303-322); D. Finkelstein: Quantum sets, assemblies and plexi (pp. 323-331); G. Kalmbach: Omologic as a Hilbert type calculus (pp. 333-340); S. Gudder: Measure and integration in quantum set theory (pp. 341-352); M. Maczynski: Commutativity and generalized transition probability in quantum logic (pp. 355-364); S. Gudder: Representations of Baer *- semigroups and quantum logics in Hilbert space (pp. 365-373); R. Greechie: A non-standard quantum logic with a strong set of states (pp. 375-380); D. Aerts: Description of compound physical systems and logical interaction of physical systems (pp. 381-403); A. Zecca: Products of logics (pp. 405-412); A. Marlow: Space time structure from quantum logic (pp. 413-418); W. Cegla: Causal logic of Minkowski space-time (pp. 419-424); M. Banai: Propositional systems in field theories and lattice-valued quantum logics (pp. 425-435); P. Kruszynski: Non-linear integration and signed measures on von Neumann algebras (pp. 437-445); P. Lahti: On the inter-relations of the three quantal principles (pp. 447-454); E. Beltrametti and G. Cassinelli: On the non-unique decomposability of quantum mixtures (pp. 455-464); B. Mielnik: Motion and form (pp. 465-477).
Reviewer: I.G.Kalmar

MSC:

03G12 Quantum logic
00Bxx Conference proceedings and collections of articles
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
81P20 Stochastic mechanics (including stochastic electrodynamics)
03-06 Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations
81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory