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A generalized modal logic in causal structures. (English) Zbl 1417.68217

Summary: Recently, a comparison between causality in the theory of relativity and in distributed computing systems as causal nets has been carried out [P. Panangaden, Theor. Comput. Sci. 546, 10–16 (2014; Zbl 1360.68634)]. In this paper, the theory of covering-based rough sets as an appropriate and comprehensive framework is applied to study causality in both branches. As a result, by future and past covering approximation operators, we propose a generalized modal logic on causal nets.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03B45 Modal logic (including the logic of norms)
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
83C75 Space-time singularities, cosmic censorship, etc.

Citations:

Zbl 1360.68634
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References:

[1] Balaguer, S.; Chatain, T.; Haar, S., Building occurrence nets from reveals relations, Fund. Inform., 290, 1, 1-5 (2012)
[2] Beem, J. K.; Ehrlich, P. E.; Easley, K. L., Global Lorentzian Geometry (1981), Marcel Dekker: Marcel Dekker New York · Zbl 0462.53001
[3] Bernardinello, L.; Ferigato, C.; Pomello, L., An algebraic model of observable properties in distributed systems, Theoret. Comput. Sci., 290, 1, 637-668 (2003) · Zbl 1019.68004
[4] Bernardinello, L.; Pomello, L.; Rombola, S., Orthomodular lattices induced by the concurrency relation, Electron. Proc. Theor. Comput. Sci., 9, 12-21 (2009) · Zbl 1456.68113
[5] Bernardinello, L.; Pomello, L.; Rombola, S., Closure operators and lattices derived from concurrency in posets and occurrence nets, Fund. Inform., 105, 3, 211-235 (2010) · Zbl 1209.68333
[6] Bernardinello, L.; Ferigato, C.; Pomello, L., Between quantum logic and concurrency, Electron. Proc. Theor. Comput. Sci., 158, 65-75 (2014) · Zbl 1464.68229
[7] Chellas, B. F., Modal Logic an Introduction (1980), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0431.03009
[8] Cegła, W.; Jadczyk, A. Z., Causal logic of Minkowski space, Comm. Math. Phys., 57, 213-317 (1977) · Zbl 0393.03046
[9] Cegła, W.; Florek, J., Orthomodular lattices generated by graphs of functions, Comm. Math. Phys., 259, 363-366 (2005) · Zbl 1079.81007
[10] Cegła, W.; Florek, J., Ortho and causal closure as a closure operations in the causal logic, Internat. J. Theoret. Phys., 44, 11-19 (2005) · Zbl 1098.81013
[11] Cegła, W.; Florek, J., The covering law in orthomodular lattices generated by graphs of functions, Comm. Math. Phys., 268, 853-856 (2006) · Zbl 1127.06005
[12] Cegła, W.; Janccewicz, B., Non-modular lattices generated by the causal structure, J. Math. Phys., 54, 122501-122505 (2013)
[13] Duntsch, I., A logic for rough sets, Theoret. Comput. Sci., 179, 1-2, 427-436 (1997) · Zbl 0896.03050
[14] Estaji, A. A.; Khodaii, S.; Bahrami, S., On rough set and fuzzy sublattice, Inform. Sci., 181, 18, 3981-3994 (2011) · Zbl 1242.06008
[15] Estaji, A. A.; Hooshmandasl, M. R.; Davvaz, B., Rough set theory applied to lattice theory, Inform. Sci., 200, 108-122 (2012) · Zbl 1248.06003
[16] Feng, T.; Zhang, S. P.; Mi, J. S., The reduction and fusion of fuzzy covering systems based on the evidence theory, Internat. J. Approx. Reason., 53, 87-103 (2012) · Zbl 1242.68326
[17] Foulis, D. J.; Randall, C. H., The empirical logic approach to the physical sciences, (Foundations of Quantum Mechanics and Ordered Linear Spaces, vol. 29 (1972), Springer), 230-249
[18] Koppitz, J.; Denecke, K., Closure Operators and Lattices, 29-47 (2006), Springer
[19] Li, T. J.; Leung, Y.; Zhang, W. X., Generalized fuzzy rough approximation operators based on fuzzy coverings, Internat. J. Approx. Reason., 48, 836-856 (2008) · Zbl 1186.68464
[20] Liu, G.; Sai, Y., A comparison of two types of rough sets induced by coverings, Internat. J. Approx. Reason., 50, 521-528 (2009) · Zbl 1191.68689
[21] Orlowska, E., Logical aspects of learning concepts, Internat. J. Approx. Reason., 2, 349-364 (1988) · Zbl 0656.68094
[22] Panangaden, P., Causality in physics and computation, Int. J. Theor. Comput. Sci., 546, 10-16 (2014) · Zbl 1360.68634
[23] Pawlak, Z., Rough sets, Int. J. Comput. Inform. Sci., 11, 341-356 (1982) · Zbl 0501.68053
[24] Pawlak, Z., Rough logic, Bull. Pol. Acad. Sci., Tech. Sci., 35, 253-258 (1987) · Zbl 0645.03019
[25] Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, vol. 9 (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, The Netherlands
[26] Penrose, R., Techniques of Differential Topology in Relativity (1972), Society for Applied and Industrial Mathematics · Zbl 0321.53001
[27] Peters, J. F.; Skowron, A.; Suraj, Z.; Ramanna, S., Guarded transitions in rough Petri nets, (Proc. of 7th European Congress on Intelligent Systems and Soft Computing. Proc. of 7th European Congress on Intelligent Systems and Soft Computing, EUFIT99, 13-16 Sept., Aachen, Germany (1999)), 203-212
[28] Peters, J. F.; Skowron, A.; Suraj, Z.; Ramanna, S., Sensor and filter models with rough Petri nets, Fund. Inform., 47 (2001) · Zbl 1004.68116
[29] Restrepo, M.; Cornelis, C.; Gómez, J., Duality,conjugacy and adjointness of approximation operators in covering-based rough sets, Internat. J. Approx. Reason., 55, 469-485 (2014) · Zbl 1316.03033
[30] Slimani, T., RST approach for efficient CARs mining, Bonfring Int. J. Data Min., 4 (2014)
[31] Sorkin, R., Spacetime and causal sets, (D’Olivo, J.; etal., Relativity and Gravitation: Classical and Quantum (1991), World Scientific) · Zbl 0972.83573
[32] Yang, T.; Li, Q. G., Reduction about approximation spaces of covering generalized rough sets, Internat. J. Approx. Reason., 51, 335-345 (2010) · Zbl 1205.68433
[33] Yao, Y. Y.; Lin, T. Y., Generalization of rough sets using modal logic, J. Intell. Autom. Soft Comput., 2, 103-120 (1996)
[34] Yao, Y.; Yao, B., Covering based rough set approximations, Inform. Sci., 200, 91-107 (2012) · Zbl 1248.68496
[35] Zhu, P.; Wang, Fei-Yue, A new type of covering rough set, (3rd International IEEE Conference Intelligent Systems (2006)), 444-449
[36] Zhu, P.; Wang, Fei-Yue, On three types of covering-based rough sets, Trans. Knowl. Data Eng., 19, 1131-1144 (2007)
[37] Zhu, W., Relationship among basic concepts in covering-based rough sets, Inform. Sci., 179, 2478-2486 (2009) · Zbl 1178.68579
[38] Zhu, P., Covering rough sets based on neighborhoods: an approach without using neighborhoods, Internat. J. Approx. Reason., 52, 461-472 (2011) · Zbl 1229.03047
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