Ultraproduct for Quantum Structures
DOI:
https://doi.org/10.12775/LLP.2018.005Keywords
Quantum Kripke frame, state space, ultraproductAbstract
Quantum Kripke frames are certain quantum structures recently introduced by Zhong. He has defined certain properties such as Existence of Approximation and Superposition for these structures. In this paper, we define the ultraproduct for the family of quantum Kripke frames and show that the aforementioned properties are invariant under ultraproduct. In this way we prove that the ultraproduct of each family of quantum Kripke frames is also a quantum Kripke frame. We also show the same results for other related quantum structures.
References
Baltag, A., and S. Smets, “Complete axiomatizationsof quantum actions”, International Journal of Theoretical Physics 44, 12 (2005): 2267–2282. DOI: 10.1007/s10773-005-8022-2
Bergfeld, J.M., K. Kishida, J. Sack, and S. Zhong, “Duality for the logic of quantum actions”, Studia Logica 103, 4 (2015): 781–805. DOI: 10.1007/s11225-014-9592-x
Birkhoff, G., and J. von Neumann, “The logic of quantum mechanics”, Annals of Mathematics 37 (1936): 823–843.
Blackburn, P., F. Wolter, and J. von Benthem, Handbook of Modal Logic, Elsevier, Amesterdam, 2007.
Blackburn, P., M. de Rijke, and Y. Venema, Modal Logic, Cambridge University Press, 2001. DOI: 10.1017/CBO9781107050884
Chang, C., and H. Keisler, Model Theory, North-Holland, Amsterdam, 1973.
Goranko, V., and M. Otto, “Model theory of modal logics”, in P. Blackburn, F. Wolter and J. von Benthem (eds.), Handbook of Modal Logic, Elsevier, Amesterdam, 2006. DOI: 10.1016/S1570-2464(07)80008-5
Hedlkova, J. ., and S. Pulmannova, “Orthogonality spaces and atomistic orthocomplemented lattices”, Czechoslovak Mathematical Journal 41 (1991): 8–23.
Hodges, W., Model Theory, Cambridge University Press, Cambridge, 1993.
Kracht, M., Tools and Techniques in Modal Logic, Elsevier, Amesterdam, 1999.
Piron, C., Foundations of Quantum Physics, W.A. Benjamin Inc., 1976.
Zhong, Sh., Orthogonality and Quantum Geometry, Towards a Relational Reconstruction of Quantum Theory, ILLC Dissertation Series, 2015.
Zhong, Sh., “Correspondence between Kripke frames and projective geometries”, Studia Logica 106, 1 (2018): 167–190. DOI: 10.1007/s11225-017-9733-0
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 719
Number of citations: 0
