Abstract
“Quantum logic” is considered here, following the main usage in the literature (Beltrametti and van Fraassen (1981)), to he the formal structure of a language which is appropriate for describing quantum physical systems and their properties. Besides its syntax this quantum language comprises a semantics which takes into account the particular conditions of quantum physical propositions and which establishes an adequate concept of truth for these propositions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beltrametti, E. and van Fraassen, B.C.: 1981, ‘Current Issues in Quantum Logic’, Plenum Press, New York
Birkhoff, G. and von Neumann, J.: 1936, ‘The Logic of Quantum Mechanics’, Ann. Math. 37, 823–843.
Curry, H.B.:1977, ‘Foundations of Mathematical Logic’, Dover Publications, New York.
Foulis, D.J. and Randall, C.H.: 1981, Empirical Logic and Tensor Products, in Neumann, H. (ed.): ‘Interpretations and Foundations of Quantum Theory’, Bibliographisches Institut, Mannheim, 9–20.
Jauch, J.M.: 1968, ‘Foundations of Quantum Mechanics’, Addison-Wesley, Reading, Mass.
Lorenzen, P. and Lorenz K.: 1978, ‘Dialogische Logik’, Wissenschaftliche Buchgesellschaft, Darmstadt.
Mackey, G.: 1963, ‘Mathematical Foundations of Quantum Mechanics’, Benjamin, New York.
Mittelstaedt, P.: 1976, ‘Philosophische Probleme der modernen Physik’, Bibliographisches Institut, Mannheim, English translation: Philosophical Problems in Modern Physics, D. Reidel Publ. Co., Dordrecht, Holland, 1976, Ch. VI.
Mittelstaedt, P.: 1978, ‘Quantum Logic’, D. Reidel Publ. Co., Dordrecht, Holland.
Mittelstaedt, P.: 1983a, ‘Relativistic Quantum Logic’, Int. J. of Th. Phys. 22, 293 – 384.
Mittelstaedt, P.: 1983b, ‘Wahrheit. Wirklichkeit und Logik in der Sprache der Physik’, Zeitschrift fur Allg. Wissen-schaftstheorie XIV, 24–45.
Piron, C.: 1976, ‘Foundations of Quantum Physics’. Benjamin, Reading, Mass.
Randall, C.H. and Foulis, D.J.: 1983, ‘Properties and Operational Propositions in Quantum Mechanics’, Found, of Phys. 13, 843–858.
Rasiowa, H.: 1974, ‘An Algebraic Approach to Non-Classical Logics’, North-Holland Publ. Co.
Stachow, E.-W.: 1976, ‘Completeness of Quantum Logic’, J. of Phil. Logic 5, 237- 280. Reprinted in C.A. Hooker (ed.): Physical Theory as Logico Operational Structure, D. Reidel Publ. Co., 1979, 203 – 243.
Stachow, E.-W.: 1980, ‘Logical Foundation of Quantum Mechanics’, Int. J. of Th. Phys. 19, 251 – 304.
Stachow, E.-W.: 1981, ‘Die quantenlogische Wahrscheinlich-keitskalkiil’, in J. Nitsch, J. Pfarr and E.-W. Stachow (eds): Grundlagenprobleme der modernen Physik, Bibliographisches Institut, Mannheim, 271 - 305.
Stachow, E.-W.: 1985, ‘Logische Grundlagen der Quantenphysik’, Bibliographisches Institut, Mannheim, in preparation.
Varadarajan, V.: 1968, 1970, ‘Geometry of Quantum Theory’.I and II, Van Nostrand, Princeton, N.J.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Stachow, EW. (1984). Classical and Non Classical Limiting Cases of Quantum Logic. In: Balzer, W., Pearce, D.A., Schmidt, HJ. (eds) Reduction in Science. Synthese Library, vol 175. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6454-9_20
Download citation
DOI: https://doi.org/10.1007/978-94-009-6454-9_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6456-3
Online ISBN: 978-94-009-6454-9
eBook Packages: Springer Book Archive