Quantum Logic and Quantum Theory in a Game-Theoretic Perspective

Open Systems and Information Dynamics

Volumn 9, Issue 3, 2002, Pages 273-290

  Pietarinen, Ahti ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347309464     PISSN: 12301612     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019712730037     Document Type: Article

References (44)

1. J. S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics 1, 195 (1964).
2. G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Annales Mathematicae 37, 823 (1936).
3. A. Boukas, Quantum formulation of classical two-person zero-sum games, Open Sys. Information Dyn. 7, 19 (2000).
4. J. Bub, Interpreting the Quantum World, Cambridge University Press, Cambridge, 1997.
5. J. F. Clauser and M. A. Home, Experimental consequences of objective local theories, Physical Review D 10, 526 (1974).
6. M. L. Dalla Chiara, Quantum Logic, in: Handbook of Philosophical Logic 3, D. Gabbay and F. Guenthner, eds., Reidel, Dordrecht, 1984, pp. 427-469.
7. M. L. Dalla Chiara and R. Giuntini, Paraconsistent ideas in quantum logic, Synthese 125, 55 (2000).
8. M. L. Dalla Chiara and R. Giuntini, Quantum Logic, in: Handbook of Philosophical Logic, 6, D. Gabbay and F. Guenthner, eds., 2-nd ed., Reidel, Dordrecht, 2002, pp. 129-228.
9. D. Deutsch, Quantum theory of probabilities and decisions, Proceedings of the Royal Society of London A 455, 3129 (1999).
10. D. Deutsch, A. Ekert, and R. Lupacchini, Machines, logic and quantum physics, Bulletin of Symbolic Logic 6, 265 (2000).
11. D. Dieks and P. E. Vermaas, The Modal Interpretation of Quantum Mechanics, Kluwer, Dordrecht, 1998.
12. A. Einstein, B. Podolsky, and N. Rosen, Can quantum mechanical description of physical reality be considered complete?, Physical Review 47, 777 (1935).
13. B. C. van Fraassen, Semantic analysis of quantum logic, in: Contemporary Research in the Foundations and Philosophy of Quantum Theory, C. A. Hooker, ed., Reidel, Dordrecht, 1973, pp. 80-113.
14. B. R. Frieden and B. H. Soffer, Lagrangians of physics and the game of Fisher-information transfer, Physical Review, E 52, 2274 (1995).
15. R. Frieden, Physics From Fisher Information, Cambridge University Press, Cambridge, 1998.
16. D. M. Greenberger, M. Horne, and A. Zeilinger, Going beyond Bell's theorem, in: Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed., Kluwer, Dordrecht, 1989, pp. 69-72.
17. S. F. Gudder, Quantum probability spaces, American Mathematical Society 21, 296 (1969).
18. G. M. Hardegree and P. J. Frazer, Charting the labyrinth of quantum logics: a progress report, in: Current Issues in Quantum Logic, E. G. Beltrametti and B. C. van Fraassen, eds., Plenum Press, New York, 1981, pp. 53-76.
19. J. Hintikka, The Principles of Mathematics Revisited, Cambridge University Press, New York, 1996.
20. J. Hintikka and G. Sandu, Game-theoretical semantics, in: Handbook of Logic and Language, J. van Benthem and A. ter Meulen, eds., Elsevier, Amsterdam, 1997, pp. 361-410.
21. C. A. Hooker, Bell, book and candle: the limning of a mystery, in: Bell's Theorem, Quantum Theory and the Conceptions of the Universe, M. Kafatos, ed., Kluwer, Dordrecht, 1989.
22. R. I,. G. Hughes, Semantic alternatives in partial Boolean algebras, Journal of Philosophical Logic 14, 411 (1985).
23. R. I. G. Hughes, The Structure and Interpretation of Quantum Mechanics, Harvard University Press, Cambridge, 1989.
24. S. Kochen and E. P. Specker, The problem of hidden variables in quantum mechanics, Journal of Mathematics and Mechanics 17, 59 (1967).
25. H. Krips, Conditionals, probability and Bell's theorem, in: Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed., Kluwer, Dordrecht, 1989, pp. 105-116.
26. H. Kuhn, Extensive games and the problem of information, in: Contributions to the Theory of Games 2, H. Kuhn and A. W. Tucker, eds., Princeton University Press, Princeton, 1953, pp. 193-216.
27. H. Kuhn, ed., Classics in Game Theory, Princeton University Press, Princeton, 1997.
28. N. D. Mermin, Hidden variables and the two theorems of John Bell, Reviews of Modern Physics 65, 803 (1993).
29. P. Mittelstaedt, Quantum Logic, Reidel, Dordrecht, 1978.
30. J. von Neumann, Zur Theorie der Gesellschaftsspiele, Mathematische Annalen 100, 295 (1928), translation by S. Bargmann, On the theory of games of strategy, in: Contributions to the Theory of Games 4, A. W. Tucker and R. D. Luce, eds., Princeton University Press, Princeton, 1959, pp. 13-42.
31. J. von Neumann, Zur Theorie der Gesellschaftsspiele, Mathematische Annalen 100, 295 (1928), translation by S. Bargmann, On the theory of games of strategy, in: Contributions to the Theory of Games 4, A. W. Tucker and R. D. Luce, eds., Princeton University Press, Princeton, 1959, pp. 13-42.
32. J. von Neumann, Communication on the Borel notes, Econometrica 21, 124 (1953).
33. J. von Neumann, Mathematical Structures of Quantum Mechanics, Princeton University Press, Princeton, 1955.
34. M. Pavicić and N. D. Megill, Non-orthomodular models for both standard quantum logic and standard classical logic: repercussions for quantum computers, Helvetica Physica Acta 72, 189 (1999).
35. J.-W. Pan et al., Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement, Nature 403, 515 (2000).
36. A. Pietarinen, Logic and coherence in the light of competitive games, to appear in Logique et Analyse 43, (2000).
37. A. Pietarinen, A note on the structural notion of information in extensive games, to appear in Quality & Quantity (2002).
38. H. Putnam, Is logic empirical?, in: Boston Studies in the Philosophy of Science 5, R. Cohen and M. Wartofsky, eds., Reidel, Dordrecht, 1969, pp. 181-206.
39. M. Rédei, Logical independence in quantum logic, Foundations of Physics 25, 411 (1995).
40. C. A. Sackett et al., Experimental entanglement of four particles, Nature 404, 256 (2000).
41. G. Sandu and A. Pietarinen, Partiality and games: Prepositional logic, Logic Journal of the IGPL 9, 107 (2001).
42. A. Shimony, Events and processes in the quantum world, in: Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds., Clarendon Press, Oxford, 1986, pp. 182-203.
43. F. R. Thompson, Equivalence of games in extensive form, RM-759, The Rand Corporation, California, 1952. (Reprinted in [27, pp. 36-45].)
44. F. R. Thompson, Equivalence of games in extensive form, RM-759, The Rand Corporation, California, 1952. (Reprinted in [27, pp. 36-45].)