### In defense of operational quantum logic

DOI: http://dx.doi.org/10.12775/LLP.2003.010

#### Abstract

#### Full Text:

PDF#### References

Aerts, D., The One and The Many, Towards a Unification of the Quantum and the Classical Description of One and Many Physical Entities, PhD-thesis, Free University of Brussels, 1981.

Aerts, D., ‘The Description of One and Many Physical Systems’ in C. Gruber, C. Piron, T.M. Tˆam, R. Weill (eds.), Les fondements de la m´ecanique quantique, 25e cours de perfectionnement de l’Association Vaudoise des Chercheurs en Physique Montana, du 6 au 12 mars 1983, l’A.V.C.P., Lausanne, 1983, pp. 63–148.

Aerts, D., B. Coecke, and S. Smets, ‘On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects’, in G.C. Cornelis, S. Smets and J.P. Van Bendegem (eds.), Metadebates on Science, The Blue Book of ‘Einstein Meets Magritte’, VUB University Press/Kluwer Academic Publishers, Brussels/Dordrecht, 1999, pp. 291-302.

Balzer, W., ‘Piron’s Foundation of Quantum Mechanics (Comment on his Paper)’, Erkenntnis 16 (1981), 403-406.

Birkhoff, G., and J. von Neumann, ‘The Logic of Quantum Mechanics’, Annals of Mathematics 37 (1936), 823–843; reprinted in C.A. Hooker (ed.), The Logico-algebraic Approach to Quantum Mechanics, vol. 1, D. Reidel Publishing Company, Dordrecht, 1975, pp. 1–26.

Carnap, R., ‘Testability and Meaning’, Philosophy of Science 3 (1936), 419–417.

Cattaneo, G., T. Marsico, and G. Nistic´o, ‘Individual Samples, Preparations, and States in Piron’s Approach to Quantum Physics’, Foundations of Physics 24 (1994), 1293–1303.

Cattaneo, G., and G. Nistic´o, ‘Axiomatic Foundations of Quantum Physics: Critiques and Misunderstandings. Piron’s Question-Proposition System’, International Journal of Theoretical Physics 30 (1991), 1293–1336.

Cattaneo, G., and G. Nistic´o, ‘A Model of Piron’s Preparation-Question Structures in Ludwig’s Selection Structures’, International Journal of Theoretical Physics 32 (1993), 407–431.

Coecke, B., D. J. Moore, and S. Smets, ‘From Operationality to Logicality: Philosophical and Formal Preliminaries’, submitted for publication.

Coecke, B., D. J. Moore, and S. Smets, ‘From Operationality to Logicality: Syntax and Semantics’, submitted for publication.

Coecke, B., D. J. Moore, and S. Smets, ‘Logic of Dynamics & Dynamics of Logic; Some Paradigm Examples’, in D. Gabbay, S. Rahman, J.M. Torres, and J.P. Van Bendegem, (eds.), Logic, Epistemology and the Unity of Science, to appear, arXiv: math.LO/0106059.

Coecke, B., D. Moore, and A. Wilce, ‘Operational Quantum Logic: An Overview’, in B. Coecke, D. Moore, and A. Wilce, (eds.), Current Research in Operational Quantum Logic: Algebras, Categories, Languages, Kluwer Academic Publishers, Dordrecht, 2000, pp. 1–36.

Coecke, B., and S. Smets, ‘A Logical Description for PerfectMeasurements’, International Journal of Theoretical Physics 39 (2000), 591–599, arXiv:quantph/0008017.

Coecke, B., and S. Smets, ‘The Sasaki Hook is not a [Static] Implicative Connective but Induces a Backward [in Time] Dynamic One that Assigns Causes’, submitted for publication, arXiv:quant-ph/0111076.

Einstein, A., B. Podolsky, and N. Rosen, ‘Can Quantum-Mechanical Description of Physical Reality be Considered Complete?’, Physical Review, 47, 777-80 (1935), reprinted in J.A. Wheeler and W.H. Zurek (eds.), Quantum Theory and Measurement, Princeton University Press, New Jersey, 1983, pp. 138–141.

Essler, W. K., and G. Zoubek, ‘Piron’s Approach to the Foundations of Quantum Mechanics’, Erkenntnis 16 (1981), 411–418.

Foulis, D., C. Piron, and C. Randall, ‘Realism, Operationalism, and Quantum Mechanics’, Foundations of Physics 13 (1983), 813–841.

Foulis, D. J., and C.H. Randall, ‘A Note on Misunderstandings of Piron’s Axioms for Quantum Mechanics’, Foundations of Physics 14 (1984), 65–81.

Hadjisavvas, N., and F. Thieffine, ‘Piron’s Axioms for Quantum Mechanics: A Reply to Foulis and Randall’, Foundations of Physics 14 (1984), 83–88.

Hadjisavvas, N., F. Thieffine, and M. Mugur-Sch¨achter, ‘Study of Piron’s System of Questions and Propositions’, Foundations of Physics 10 (1980), 751–765.

Jauch, J.M., Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts, 1968.

Jauch, J.M., and C. Piron, ‘Can Hidden Variables be Excluded in Quantum Mechanics?’, Helvetica Physica Acta 36 (1963), 827–837.

Jauch, J.M., and C. Piron, ‘On the Structure of Quantal Proposition Systems’, Helvetica Physica Acta 42 (1969), 842–848.

Moore, D. J., ‘On State Spaces and Property Lattices’, Studies in History and Philosophy of Modern Physics 30 (1999, 61–83.

Niiniluoto, I., ‘Varieties of Realism’, in P. Lahti and P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics, 1987, The Copenhagen Interpretation 60 Years after the Como Lecture, Joensuu, Finland, 6–8 August 1987, World Scientific, Singapore, 1987.

Niiniluoto, I., Critical Scientific Realism, Oxford University Press, UK, 1999.

Piron, C., ‘Axiomatique quantique (PhD-Thesis)’, Helvetica Physica Acta 37 (1964), 439–468, English Translation by M. Cole: ‘Quantum Axiomatics’ RB4 Technical memo 107/106/104, GPO Engineering Department (London).

Piron, C., ‘Survey of General Quantum Physics’, Foundations of Physics 2 (1972), 287–314, reprinted in C.A. Hooker (ed.), The Logico-Algebraic Approach to Quantum Mechanics, vol I, D. Reidel Publishing Company, Dordrecht, 1975.

Piron, C., Foundations of Quantum Physics, W.A. Benjamin Inc., Massachusetts, 1976.

Piron, C., ‘Ideal Measurement and Probability in Quantum Mechanics’, Erkenntnis, 16 (1981), 397–401.

Piron, C., ‘Quantum Mechanics Fifty Years After’, in P. Lahti and P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics, World Scientific, 1985, pp. 207–211.

Piron, C., M´ecanique quantique. Bases et applications, Presses polytechniques et universitaires romandes, Lausanne (Second corrected edition 1998) First Edition, 1990.

Piron, C., ‘Quoi de neuf en physique quantique?’, Note Mat. Fis. Ed. Cerfim 5 (1991), 139–152.

Randall, C.H., and D. J. Foulis, ‘Properties and Operational Propositions in Quantum Mechanics’, Foundations of Physics 13 (1983), 843–857.

Smets, S., The Logic of Physical Properties in Static and Dynamic Perspective, PhD-thesis, Free University of Brussels, 2001.

Smets, S., ‘The Epistemology behind Operational Quantum Logic’, Foundations of Science, submitted for publication, 2002.

Thieffine, F., N. Hadjisavvas, and M. Mugur-Sch¨achter, ‘Supplement to a critique of Piron’s system of questions and propositions’, Foundations of Physics 11 (1981), 645–649.

Valckenborgh, F., ‘Operational Axiomatics and Compound Systems’, in B. Coecke, D. Moore, and A. Wilce, Current Research in Operational Quantum Logic: Algebras, Categories, Languages, Kluwer Academic Publishers, Dordrecht, 2000, pp. 219-244.

Valckenborgh, F., Compound Systems in Quantum Axiomatics, Analysis of Subsystem Recognition and Classification of the Various Products from a Categorical Perspective, PhD-thesis, Free University of Brussels, 2001.

Print ISSN: 1425-3305

Online ISSN: 2300-9802