In this paper, using the language of spin-half particles, Hardy’s paradox is examined within different semantics: a partial one, a many-valued one, and the one defined as a set of weak values of projection operators. As it is shown in this paper, any of such non-classical semantics can resolve Hardy’s paradox.
REFERENCES
1.
L.
Hardy
, “Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories
,” Phys. Rev. Lett.
68
(20
), 2981
–2984
(1992
).2.
Y.
Aharonov
, A.
Botero
, S.
Popescu
, R.
Reznik
, and J.
Tollaksen
, “Revisiting Hardy’s paradox: Counterfactual statements, real measurements, entanglement and weak values
,” Phys. Lett. A
301
, 130
–138
(2002
).3.
R.
Griffiths
, Consistent Quantum Theory
, Hardy’s Paradox (Cambridge University Press
, Cambridge, UK
, 2002
), Chap. 25.4.
S.
Gottwald
, A Treatise on Many-Valued Logics
(Research Studies Press Ltd.
, Baldock, Hertfordshire, England
, 2001
).5.
H.
Leblanc
, R.
Stern
, and R.
Gumb
, Essays in Epistemology and Semantics
(Haven Publications
, New York
, 1983
).6.
E.
Adams
, A Primer of Probability Logic
(University of Chicago Press
, Chicago, IL
, 1996
).7.
A.
Varzi
, “Supervaluationism and its logics
,” Mind
116
, 633
–676
(2007
).8.
9.
A.
Bolotin
, “Quantum supervaluationism
,” J. Math. Phys.
58
(12
), 122106-1
–122106-7
(2017
).10.
A.
Bolotin
, “Truth values of quantum phenomena
,” Int. J. Theor. Phys.
57
(7
), 2124
–2132
(2018
).11.
J.-Y.
Bèziau
, “Bivalence excluded middle and non contradiction
,” in The Logica Yearbook 2003
, edited by L.
Behounek
(Academy of Sciences
, Prague
, 2003
).12.
J.
Pykacz
, “Can many-valued logic help to comprehend quantum phenomena?
,” Int. J. Theor. Phys.
54
, 4367
–4375
(2015
).13.
J.
Pykacz
, Quantum Physics, Fuzzy Sets and Logic. Steps Towards a Many-Valued Interpretation of Quantum Mechanics
(Springer
, Cham
, 2015
).14.
L.
Vaidman
, “Past of a quantum particle
,” Phys. Rev. A
87
(5
), 052104-1
–052104-6
(2013
).15.
B.
Svensson
, “Quantum weak values and logic: An uneasy couple
,” Found. Phys.
47
(3
), 430
–452
(2017
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
