Approximating families for lattice outer measures on unsharp quantum logics

References

[1] Adamski, W.: On extremal extensions of regular contents and measures, Proc. Amer. Math. Soc. 121 (1994), 1159–1164.10.1090/S0002-9939-1994-1204367-3Search in Google Scholar

[2] Avallone, A.—Basile, A.: On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2003), 378–390.10.1016/S0022-247X(03)00274-9Search in Google Scholar

[3] Avallone, A.—De Simone, A.: Extensions of modular functions on orthomodular lattices, Ital. J. Pure Appl. Math. Soc. 9 (2001), 109–122.Search in Google Scholar

[4] Balcar, B.—Jech, T.: Weak Distributivity. A Problem of Von Neumann and the Mystery of Measurability, Bull. Symb. Logic 12(2) (2006), 241–266.10.2178/bsl/1146620061Search in Google Scholar

[5] Beltrametti, E. G.—Cassinelli, G.: The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts, 1981.Search in Google Scholar

[6] Bennett, M. K.—Foulis, D. J.: Phi-symmetric effect algebras, Found. Phys. 25 (1995), 1699–1722.10.1007/BF02057883Search in Google Scholar

[7] Birkhoff, G.—Neumann, J. von: The logic of quantum mechanics, Ann. Math. 37 (1936), 823–834.10.2307/1968621Search in Google Scholar

[8] Busch, P.—Lahti, P.—Mittelstaedt, P.: The Quantum Theory of Measurements. Lecture Notes in Physics, New Series m2, Springer, Berlin, 1991.10.1007/978-3-662-13844-1Search in Google Scholar

[9] Butnariu, D.—Klement, P.: Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer, Dordrecht, 1993.10.1007/978-94-017-3602-2Search in Google Scholar

[10] Chiara, M. Dalla —Giuntini, R.—Greechie, R.: Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics, Kluwer Academic Pub., Dordrecht, 2004.Search in Google Scholar

[11] Dvurečenskij, A.: On orders of observables on effect algebras, Int. J. Theor. Phys. 56 (2017), 4112–4125.10.1007/s10773-017-3472-xSearch in Google Scholar

[12] Dvurečenskij, A.—Pulmannová, S.: New Trends in Quantum Structures, Kluwer Acad. Pub., 2000.10.1007/978-94-017-2422-7Search in Google Scholar

[13] Dvurečenskij, A.—Pulmannová, S.: Difference posets, effects and quantum measurements, Int. J. Theor. Phys. 33 (1994), 819–825.10.1007/BF00672820Search in Google Scholar

[14] Foulis, D. J.—Bennett, M. K.: Effect algebras and unsharp quantum logics, Found. Phys. 10 (1994), 1331–1352.10.1007/BF02283036Search in Google Scholar

[15] Ghirardato, P.—Marinacci, M.: Ambiguity made precise: a comparative foundation, J. Econom. Theory 102 (2002), 251–289.10.4324/9780203358061_chapter_10Search in Google Scholar

[16] Kagan, E.—Ben-gal, I., Navigation of quantum-controlled mobile robots, Recent Advances in Mobile Robotics (A. Topalov, ed.), InTech, 2011, pp. 311–326.10.5772/25944Search in Google Scholar

[17] Kalmbach, G.: Orthomodular Lattices, Academic Press, London, 1983.Search in Google Scholar

[18] Khare, M.—Gupta, S.: Non-additive measures, envelops and extensions of quasi-measures, Sarajevo J. Math. 6(18) (2010), 35–49.10.5644/SJM.06.1.03Search in Google Scholar

[19] Khare, M.—Pandey, P.: Outer and inner approximations in quantum spaces, Math. Slovaca 71(1) (2021), 11–2610.1515/ms-2017-0449Search in Google Scholar

[20] Khare, M.—Shukla, A.: Extensions and measurability in quantum measure spaces, Math. Slovaca 66(2) (2016), 367–378.10.1515/ms-2015-0142Search in Google Scholar

[21] Khare, M.—Singh, A. K.: Weakly tight functions, their Jordan type decomposition and total variation in effect algebras, J. Math. Anal. Appl. 344(1) (2008), 535–545.10.1016/j.jmaa.2008.03.017Search in Google Scholar

[22] Khare, M.—Singh, B.—Shukla, A.: Approximation in quantum measure spaces, Math. Slovaca 68(3) (2018), 491–500.10.1515/ms-2017-0119Search in Google Scholar

[23] Kôpka, F.—Chovanec, F.: D-posets, Math. Slovaca 44 (1994), 21–34.Search in Google Scholar

[24] Ludwig, G.: Foundations of Quantum Mechanics, Vols. I and II, Springer, New York, 1983/1985.10.1007/978-3-642-86754-5Search in Google Scholar

[25] Riečan, B.: The measure extension theorem for subadditive probabilty measures in orthomodular σ-continuous lattices, Comm. Math. Univ. Carolin. 202 (1979), 309–315.Search in Google Scholar

[26] Shanga, Y.—Lua, X.—Lua, R.: A theory of computation based on unsharp quantum logic: Finite state automata and pushdown automata, Theor. Comp. Sci. 434 (2012), 53–86.10.1016/j.tcs.2012.02.018Search in Google Scholar

[27] Stratigos, P. D.: Lattice seperation and outer measures, J. Math. Anal. Appl. 166 (1992), 84–102.10.1016/0022-247X(92)90328-BSearch in Google Scholar

[28] Varadarajan, V. S.: Geometry of Quantum Theory, Vol. 1, Van Nostrand, Princeton, New Jersey, 1968.10.1007/978-0-387-49386-2Search in Google Scholar

[29] Volauf, P.: Some Problems of the Probability Theory in Ordered Spaces, Ph.D. Dissertation, Bratislava, 1977.Search in Google Scholar

[30] Yali, W.—Yichuan, Y.: Notes on quantum logics and involutive bounded posets, Soft Comput. 21 (2017), 2513–2519.10.1007/s00500-017-2579-6Search in Google Scholar