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Articles

Towards many-valued/fuzzy interpretation of quantum mechanics

Pages 11-21 | Received 30 Sep 2008, Accepted 19 Aug 2009, Published online: 12 Aug 2010

References

  • Birkhoff , G. and von Neumann , J. 1936 . The logic of quantum mechanics . Annals of mathematics , 37 : 823 – 843 .
  • Frink , O. 1938 . New algebras of logic . American mathematics monthly , 45 : 210 – 219 .
  • Giles , R. 1976 . Łukasiewicz logic and fuzzy set theory . International journal of man–machine studies , 67 : 313 – 327 .
  • Łukasiewicz , J. 1913 . Die logischen Grundlagen der Wahrscheinlichkeitsrechnung , 16 – 63 . Kraków : Acad. der Wiss. . reprinted as: Logical foundations of probability theory, in Łukasiewicz (1970)
  • Łukasiewicz , J. 1923 . Lecture delivered at the 232nd Meeting of the Polish Philosophical Society in Lwów on October 14, 1922 . Ruch Filozoficzny , 7 : 92 – 93 . (in Polish), reprinted as: A numerical interpretation of the theory of propositions, in Łukasiewicz (1970), 129–130
  • Łukasiewicz , J. 1970 . Selected works , Edited by: Borkowski , L. Amsterdam/Warszawa : North-Holland/PWN – Polish Scientific Publishers .
  • M czyński, M.J., 1973. The orthogonality postulate in axiomatic quantum mechanics. International journal of theoretical physics, 8, 353–360
  • M czyński, M.J., 1974. Functional properties of quantum logics. International journal of theoretical physics. 11, 149–156
  • Peres , A. 1978 . Unperformed experiments have no results . American journal of physics , 46 : 745 – 747 .
  • Pták , P. and Pulmannová , S. 1991 . Orthomodular structures as quantum logics , Dordrecht : Kluwer Academic Publishers .
  • Pykacz , J. 1987 . “ Quantum logics as families of fuzzy subsets of the set of physical states ” . In Preprints of the second international fuzzy systems association congress Vol. 2 , 437 – 440 . Tokyo, July 20–25
  • Pykacz , J. 1992 . Fuzzy set ideas in quantum logics . International journal of theoretical physics , 31 : 1767 – 1783 .
  • Pykacz , J. 1994 . Fuzzy quantum logics and infinite-valued Łukasiewicz logic . International journal of theoretical physics , 33 : 1403 – 1416 .
  • Pykacz , J. 2003 . The many-valued logic of Jan Łukasiewicz in the foundations of quantum mechanics , Gdańsk : Wydawnictwo Uniwersytetu Gdańskiego .
  • Zadeh , L.A. 1965 . Fuzzy sets . Information and control , 8 : 338 – 353 .
  • Zawirski , Z. 1934 . Relationship between many-valued logic and the calculus of probability . Prace Komisji Filozoficznej Poznańskiego Towarzystwa Przyjaciół Nauk , 4 : 155 – 240 . (in Polish)

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