Linked bibliography for the SEP article "Quantum Logic and Probability Theory" by Alexander Wilce

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

This experiment has been authorized by the editors of the Stanford Encyclopedia of Philosophy. The original article and bibliography can be found here.

Abramsky, Samson and Bob Coecke, 2009, “Categorical Quantum Mechanics”, in Engesser, Gabbay, and Lehmann 2009: 261–323. doi:10.1016/b978-0-444-52869-8.50010-4 (Scholar)
Aerts, Diederik, 1981, The One and the Many: Towards a Unification of the Quantum and Classical Description of One and Many Physical Entities, Ph.D. Dissertation, Free University of Brussels. (Scholar)
Amemiya, Ichiro and Huzihiro Aaraki, 1966, “A Remark on Piron’s Paper”, Publications of the Research Institute for Mathematical Sciences (Series A), 2(3): 423–427. doi:10.2977/prims/1195195769 (Scholar)
Baez, John, 2006, “Quantum Quandaries: a Category-Theoretic Perspective”, in Steven French, Dean Rickles, and Juha Saatsi (eds), Structural Foundations of Quantum Gravity, Oxford: Oxford University Press, 240-265. doi:10.1093/acprof:oso/9780199269693.003.0008. (Scholar)
Bacciagaluppi, Guido, 2009, “Is Logic Empirical?” in Engesser, Gabbay, and Lehmann 2009: 49–78. doi:10.1016/b978-0-444-52869-8.50006-2 (Scholar)
Baltag, A. and S. Smets, 2005, “Complete Axiomatizations for Quantum Actions”, International Journal of Theoretical Physics, 44(12): 2267–2282. doi:10.1007/s10773-005-8022-2 (Scholar)
Beltrametti, Enrico G. and Gianni Cassinelli, 1981, The Logic of Quantum Mechanics (Encyclopedia of Mathematics and its Applications, Volume 15), Reading, MA: Addison-Wesley. (Scholar)
Birkhoff, Garrett, 1967, Lattice Theory, Providence: American Mathematical Society. (Scholar)
Birkhoff, Garrett and John von Neumann, 1936, “The Logic of Quantum Mechanics”, Annals of Mathematics, 37(4): 823–843. doi:10.2307/1968621 (Scholar)
Chiribella, Giulio, Giacomo Mauro D’Ariano, and Paolo Perinotti, 2011, “Informational Derivation of Quantum Theory”, Physical Review A, 84(1): 012311. doi:10.1103/physreva.84.012311 (Scholar)
Clifton, Rob and Adrian Kent, 2000, “Simulating Quantum Mechanics by Non-Contextual Hidden Variables”, Proceedings of the Royal Society A, 456: 2101–2114. doi:10.1098/rspa.2000.0604 (Scholar)
Coecke, Bob, 2011, “A Universe of Processes and Some of Its Guises”, in Hans Halvorson (ed.), Deep Beauty: Understanding the Quantum World Through Mathematical Innovation, Cambridge: Cambridge University Press, pp. 129–186. (Scholar)
Cohen, David W. and George Svetlichny, 1987, “Minimal Supports in Quantum Logics”, International Journal of Theoretical Physics, 26(5): 435–450. doi:10.1007/bf00668776 (Scholar)
Cooke, Roger M. and J. Hilgevoord, 1981, “A New Approach to Equivalence in Quantum Logic”, in Enrico G. Beltrammetti and Bas C. van Fraassen (eds.) Current Issues in Quantum Logic, New York: Plenum, pp. 101–113. doi:10.1007/978-1-4613-3228-2_7 (Scholar)
Dakic, Borivoje, and Caslav Brukner, 2011, “Quantum Theory and Beyond: Is Entanglement Special?”, in Hans Halvorson (ed.), Deep Beauty: Understanding the Quantum World Through Mathematical Innovation, Cambridge: Cambridge University Press, pp. 129–186. doi:10.1017/cbo9780511976971.011 (Scholar)
Davey, B.A. and H.A. Priestley, 1990, Introduction to Lattices and Order, Cambridge: Cambridge University Press. (Scholar)
Engesser, Kurt, Dov M. Gabbay, and Daniel Lehmann (eds), 2009, Handbook of Quantum Logic and Quantum Structures, Amsterdam: North-Holland. (Scholar)
Fine, Arthur, 1973, “Probability and the Interpretation of Quantum Mechanics”, British Journal for the Philosophy of Science, 24(1): 1–37. doi:10.1093/bjps/24.1.1 (Scholar)
Foulis, D. J., 2000, “MV and Heyting effect algebras”, Foundations of Physics, 30: 1687–1706. (Scholar)
Foulis, D. J., and M. K. Bennett, 1994, “Effect algebras and unsharp quantum logics”, Foundations of Physics, 24: 1331–1352. doi:10.1007/bf02283036 (Scholar)
Foulis, D.J., R. Greechie, and G.T. Rüttimann, 1992, “Filters and Supports in Orthoalgebras”, International Journal of Theoretical Physics, 31(5): 789–807. doi:10.1007/bf00678545 (Scholar)
Foulis, D.J., C. Piron, and C.H. Randall, 1983, “Realism, Operationalism and Quantum Mechanics”, Foundations of Physics, 13(8): 813–841. doi:10.1007/bf01906271 (Scholar)
Foulis, D.J. and C.H. Randall, 1981a, “Empirical Logic and Tensor Products”, in Holger Neumann (ed), Interpretations and Foundations of Quantum Mechanics: Proceedings of a Conference Hold [sic] in Marburg, 28–30 May 1979 (Grundlagen der exakten Naturwissenschaften, volume 5), Mannheim: Wissenchaftsverlag, pp. 9–20. (Scholar)
–––, 1981b, “What Are Quantum Logics and What Ought They to Be?”, in Enrico G. Beltrametti and Bas C. van Fraassen (eds), Current Issues in Quantum Logic, New York: Plenum, pp. 35–52. doi:10.1007/978-1-4613-3228-2_3 (Scholar)
–––, 1984, “Stochastic Entities” in P. Mittelstaedt and E. Stachow (eds.), Recent Developments in Quantum Logic, Mannheim: B.I. Wissenschaft. (Scholar)
Giuntini, Roberto, and Hans Greuling, 1989, “Toward a formal language for unsharp properties”, Foundations of Physics, 20: 931–395. (Scholar)
Gleason, Andrew M., 1957, “Measures on the Closed Subspaces of a Hilbert Space”, Journal of Mathematics and Mechanics, 6(6): 885–893. (Scholar)
Grätzer, George, 1998, General Lattice Theory, Basel: Birkhäuser Verlag (2nd edition). (Scholar)
Golfin, Andrew S., Jr., 1988, Representations of Complete Lattices, Ph. D. Dissertation, University of Massachusetts, Amherst. (Scholar)
Gudder, Stanley P., 1970, “On Hidden-Variable Theories”, Journal of Mathematical Physics, 11(2): 431–436. doi:10.1063/1.1665156 (Scholar)
–––, 1989, Quantum Probability Theory, San Diego: Academic Press. (Scholar)
Gudder, Stan, and Richard Greechie, 2002, “Sequential products on effect algebras”, Reports on Mathematical Physics, 49(1): 87–111. doi:10.1016/s0034-4877(02)80007-6 (Scholar)
Guz, Wawrzyniec, 1978, “Filter Theory and Covering Law”, Annales de l’Institut Henri Poincaré. Section A, Physique Théorique, 29(4): 357–378. [Guz 1978 available online] (Scholar)
Harding, John, 1996, “Decompositions in Quantum Logic”, Transactions of the American Mathematical Society, 348(5): 1839–1862. doi:10.1090/s0002-9947-96-01548-6 (Scholar)
–––, 1998, “Regularity in Quantum Logic”, International Journal of Theoretical Physics, 37(4): 1173–1212. doi:10.1023/a:1026665818335 (Scholar)
–––, 2009, “A Link Between Quantum Logic and Categorical Quantum Mechanics”, International Journal of Theoretical Physics, 48(3): 769–802. doi:10.1007/s10773-008-9853-4 (Scholar)
Holevo, Alexander S., 1982, Probabilistic and Statistical Aspects of Quantum Theory, Amsterdam: North Holland. (Scholar)
Holland, Samuel S. Jr., 1995, “Quantum mechanics in Hilbert space: A result of M.P. Soler”, Bulletin of the American Mathematical Society, 32(2): 205–232. doi:10.1090/s0273-0979-1995-00593-8 (Scholar)
Ischi, Boris, 2000, “Endomorphisms of the Separated Product of Lattices”, International Journal of Theoretical Physics, 39(11): 2559–2581. doi:10.1023/a:1026405608135 (Scholar)
Jauch, J.M. and C. Piron, 1969, “On the Structure of Quantal Propositional Systems”, Helvetica Physica Acta, 42(6): 842–848. doi:10.5169/seals-114098 (Scholar)
Kalmbach, Gudrun, 1983, Orthomodular Lattices, London: Academic Press. (Scholar)
Kläy, Matthias P., 1988, “Einstein-Podolsky-Rosen Experiments: The Structure of the Sample Space I, IIç”, Foundations of Physics Letters, 1(3): 205–244. doi:10.1007/bf00690066 (Scholar)
Kochen, Simon and E.P. Specker, 1965, “Logical structures arising in quantum theory”, Symposium on the Theory of Models: Proceedings of the 1963 International Symposium [on the Theory of Models, Held] at Berkeley, [from June 25 to July 11 1963], J.W. Addison, Leon Henkin, and Alfred Tarski (eds), Amsterdam: North-Holland, pp. 177–189. (Scholar)
–––, 1967, “The Problem of Hidden Variables in Quantum Mechanics” Journal of Mathematics and Mechanics, 17: 59–87. (Scholar)
Kôpka, František, and Ferdinand Chovanec, 1994, “D-posets”, Mathematica Slovaca, 44: 21–34.
Ludwig, Günther, 1983, Foundations of Quantum Mechanics I, New York: Springer-Verlag. (Scholar)
Mackey, George W., 1957, “Quantum Mechanics and Hilbert Space”, The American Mathematical Monthly, 64(8): 45–57. doi:10.2307/2308516 (Scholar)
–––, 1963, The Mathematical Foundations of Quantum Mechanics: A Lecture-note Volume, New York: W.A. Benjamin. (Scholar)
Maudlin, Tim, 2005, “The Tale of Quantum Logic”, in Yemima Ben-Menahem (ed.), Hilary Putnam, Cambridge: Cambridge University Press, pp. 156–187. doi:10.1017/cbo9780511614187.006 (Scholar)
Massanes, Lluis, and Markus Mueller, 2011, “A Derivation of Quantum Theory from Physical Requirements”, New Journal of Physics, 13: 063001. doi:10.1088/1367-2630/13/6/063001 (Scholar)
Meyer, David A., 1999, “Finite Precision Measurement Nullifies the Kochen-Specker Theorem”, Physical Review Letters, 83(19): 3751–54. doi:10.1103/physrevlett.83.3751 (Scholar)
Piron, C., 1964, “Axiomatique Quantique”, Helvetica Physica Acta, 37(4–5): 439–468. doi:10.5169/seals-113494 (Scholar)
–––, 1976, Foundations of Quantum Physics, Reading, MA: W.A. Benjamin. (Scholar)
Pitowsky, Itamar, 1989, Quantum Probability—Quantum Logic (Lecture Notes in Physics, volume 321), Berlin: Springer-Verlag. (Scholar)
–––, 2006, “Quantum Mechanics as a Theory of Probability”, in William Demopoulos and Itamar Pitowsky (eds.) Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Dordrecht: Springer, pp. 213–240. doi:10.1007/1-4020-4876-9_10 (Scholar)
Putnam, Hilary, 1968, “Is Logic Empirical?” in R. Cohen and M.P. Wartofski (eds.), Boston Studies in the Philosophy of Science (Volume 5), Dordrecht: D. Reidel; reprinted as “The Logic of Quantum Mechanics” in Hilary Putnam, Mathematics, Matter and Method, Cambridge University Press, 1976, second edition 1979, pp. 174–197. doi:10.1017/cbo9780511625268.012 (Scholar)
Rau, Jochen, 2009, “On Quantum vs Classical Probability”, Annals of Physics, 324(12): 2622–2637. doi:10.1016/j.aop.2009.09.013 (Scholar)
Randall, C.H. and D.J. Foulis, 1983, “Properties and Operational Propositions in Quantum Mechanics”, Foundations of Physics, 13(8): 843–863. doi:10.1007/bf01906272 (Scholar)
Randall, C.H. and D.J. Foulis, 1985, “Stochastic Entities”, in Recent Developments in Quantum Logic, P. Mittelstaedt and E. Stachow (eds.), Mannheim: Bibliographisches Institut, pp. 265–284. (Scholar)
Selinger, Peter, 2007, “Dagger Compact Closed Categories and Completely Positive Maps” (Extended Abstract), Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005), Chicago. Electronic Notes in Theoretical Computer Science, 170: 139–163. doi:10.1016/j.entcs.2006.12.018 (Scholar)
van Fraassen, Bas C., 1992, Quantum Mechanics: An Empiricist View, Oxford: Oxford University Press. (Scholar)
Varadarajan, Veeravalli Sesshadri, 1985, Geometry of Quantum Mechanics, New York: Springer-Verlag. doi:10.1007/978-0-387-49386-2 (Scholar)
von Neumann, John, 1932, Mathematische Grundlagen der Quantenmechanik, Berlin: Springer-Verlag; English translation: Mathematical Foundations of Quantum Mechanics, Princeton: Princeton University Press, 1955. (Scholar)
de Wetering, John, 2019, “Sequential Product Spaces are Jordan Algebras”, Journal of Mathematical Physics, 60(6): 062201. doi:10.1063/1.5093504 (Scholar)
Wilce, Alexander, 1992, “Tensor Products in Generalized Measure Theory”, International Journal of Theoretical Physics, 31(11): 1915–1928. doi:10.1007/bf00671964 (Scholar)
–––, 2000a, “Generalized Sasaki Projections”, International Journal of Theoretical Physics, 39: 969–974. doi:10.1023/a:1003607820078 (Scholar)
–––, 2000b, “Test Spaces and Orthoalgebras”, in Bob Coecke, David Moore, and Alexander Wilce (eds), Current Research in Operational Quantum Logic, Dordrecht: Kluwer Academic Publishers, pp. 81–114. doi:10.1007/978-94-017-1201-9_4 (Scholar)
–––, 2009, “Test spaces”, Engesser, Gabbay, and Lehmann 2009: 443–549. doi:10.1016/b978-0-444-52869-8.50014-1 (Scholar)
–––, 2018, “A Royal Road to Quantum Theory (or Thereabouts)”, Entropy, 20(4): 227 doi:10.3390/e20040227 (Scholar)
Wright, Ron, 1980, “The State of the Pentagon: A Nonclassical Example”, in A.R. Marlowe (ed.), Mathematical Foundations of Quantum Physics, New York: Academic Press, pp. 255–274. doi:10.1016/b978-0-12-473250-6.50015-7 (Scholar)
Younce, Matthew B., 1987, Random Variables on Non-Boolean Structures, Ph.D. Dissertation, Department of Mathematics, University of Massachusetts/Amherst. (Scholar)

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