An overview of rough set semantics for modal and quantifier logics

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 8, Issue 1, 2000, Pages 93-118

  Liau, Churn Jung ^a  

^a INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

Author keywords

Epistemic logic; Modal logic; Rough quantifiers; Rough set

Indexed keywords

EID: 0012036553     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488500000071     Document Type: Review

References (94)

1. C.J. Liau. "On rough quantifiers". In R. Trappl, editor, Proceedings of the 14th European Meeting on Cybernetics and Systems Research, pages 175-180, 1998.
2. C.J. Liau. "Modal reasoning and rough set theory". In Proceedings of the 8th International Conference on Artificial Intelligence: Methodology, Systems, Applications, pages 317-330, LNAI 1480, Springer-Verlag, 1998. (An abstract also appears in Proc. of IPMU'98 , pages 1894-1895, Paris, 1998).
3. C.J. Liau. "Modal reasoning and rough set theory". In Proceedings of the 8th International Conference on Artificial Intelligence: Methodology, Systems, Applications, pages 317-330, LNAI 1480, Springer-Verlag, 1998. (An abstract also appears in Proc. of IPMU'98 , pages 1894-1895, Paris, 1998).
4. Z. Pawlak. "Rough sets". International Journal of Computer and Information Science, 11:341-356, 1982.
5. Z. Pawlak. Rough Sets-Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, 1991.
6. J. Komorowski, L. Polkowski, and A. Skowron. "Rough sets: a tutorial". In S.K. Pal and A. Skowron, editors, Rough-Fuzzy Hybridization: A New Method for Decision Making, Springer-Verlag, Singapore(in Print), 1998.
7. T.Y. Lin and N. Cercone, editors. Rough Sets and Data Mining-Analysis of Imprecise Data. Kluwer Academic Publishers, 1997.
8. E. Orłowska, editor. Incomplete Information: Rough Set Analysis, Volume 13 of Studies of Fuzziness and Soft Computing. Physica-Verlag, Heidelberg, Germany, 1998.
9. L. Polkowski and A. Skowron, editors. Rough Sets in Knowledge Discovery 1: Methodology and Applications, Volume 18 of Studies of Fuzziness and Soft Computing. Physica-Verlag, Heidelberg, Germany, 1998.
10. L. Polkowski and A. Skowron, editors. Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems, Volume 19 of Studies of Fuzziness and Soft Computing. Physica-Verlag, Heidelberg, Germany, 1998.
11. L. Polkowski and A. Skowron, editors. Proc. of 1st International Conference on Rough Sets and Current Trends in Computing, LNAI 1424. Springer-Verlag, Berlin, 1998.
12. D.M. Gabbay and F. Guenthner, editors. Handbook of Philosophical Logic, Vol. I-IV. D. Reidel Publishing Company, 1983.
13. R.M. Smullyan. First-order Logic. Springer-Verlag, 1968.
14. B.F. Chellas. Modal Logic : An Introduction. Cambridge University Press, 1980.
15. D.M. Gabbay, C.J. Hogger, and J.A. Robinson, editors. Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 1-4. Clarendon Press - Oxford, 1994.
16. S. Abramsky, D.M. Gabbay, and T.S.E. Maibaum, editors. Handbook of Logic in Computer Science, Vol. 1-3. Clarendon Press - Oxford, 1992.
17. E. Orłowska. "Logic of nondeterministic information". Studia Logica, XLIV:93-102, 1985.
18. E. Orłowska. "Logic of indiscernibility relation". Bulletin of the Polish Academy of Science: Mathematics, 33:473-485, 1985.
19. E. Orłowska. "Semantics of knowledge operators". Bulletin of the Polish Academy of Science: Mathematics, 35:255-264, 1987.
20. E. Orłowska. "Reasoning about vague concepts". Bulletin of the Polish Academy of Science: Mathematics, 35:643-652, 1987.
21. E. Orłowska. "Logic for reasoning about knowledge". Zeitschrift f. Math. Logik und Grundlagen der Math, 35:559-572, 1989.
22. E. Orłowska. "Kripke semantics for knowledge representation logics". Studia Logica, XLIX:255-272, 1990.
23. L. Farinas del Cerro and E. Orłowska. "DAL-A logic for data analysis". Theoretical Computer Science, 36:251-264, 1985.
24. C.M. Rauszer. "Approximation methods for knowledge representation systems". In J.Komorowski and Z. W. Raś, editors, Proceedings of the 7th ISMIS, LNAI 689, pages 326-337. Springer-Verlag, 1993.
25. C.M. Rauszer. "Rough logic for multi-agent systems". In M. Masuch and L. Pólos, editors, Knowledge Representation and Reasoning under Uncertainty, LNAI 808, pages 161-181. Springer-Verlag, 1994.
26. D. Vakarelov. "Modal logics for knowledge representation". In A.R. Meyer and M.A. Taitslin, editors, Proceedings of Symposium on Logical Foundations of Computer Science, LNCS 363, pages 257-277. Springer-Verlag, 1989.
27. B. Konikowska. "A formal language for reasoning about indiscernibility ". Bulletin of the Polish Academy of Science: Mathematics, 35:239-249, 1987.
28. Y.Y. Yao and T.Y. Lin. "Generalization of rough sets using modal logics". Intelligent Automation and Soft Computing, 2:103-120, 1996.
29. Y.Y. Yao. "Two views of the theory of rough sets in finite universes". International Journal of Approximate Reasoning, 15:291-317, 1996.
30. Y.Y. Yao, S.K.M. Wong, and T.Y. Lin. "A review of rough set models". In T.Y. Lin and N. Cercone, editors, Rough Sets and Data Mining-Analysis of Imprecise Data, pages 47-75. Kluwer Academic Publishers, 1997.
31. Z. Pawlak. "Rough logic". Bulletin of the Polish Academy of Science:Technical Science, 35:253-258, 1987.
32. M. Krynicki. "Linearly ordered quantifiers". Bulletin of the Polish Academy of Science: Mathematics, 37:295-303, 1989.
33. M. Krynicki. "Quantifiers determined by partial orderings". Zeitschrift f. Math. Logik und Grundlagen der Math, 36:79-86, 1990.
34. M. Krynicki and H.-P. Tuschik. "An axiomatization of the logic with the rough quantifier". The Journal of Symbol Logic, 56(2):608-617, 1991.
35. M.K. Chakraborty and M. Banerjee. "Rough logic with rough quantifiers". Bulletin of the Polish Academy of Science: Mathematics, 41:305-315, 1993.
36. L.W. Szczerba. "Rough quantifiers". Bulletin of the Polish Academy of Science: Mathematics, 35:251-254, 1987.
37. L. Bole and P. Borowik. Many-Valued Logics 1: Theoretical Foundations. Springer-Verlag, 1992.
38. H. Rasiowa and A. Skowron. "Rough concepts logic". In A. Skowron, editor, Proceedings of the 5th Symposium on Computation Theory, LNCS 208, pages 288-297. Springer-Verlag, 1984.
39. H. Rasiowa and A. Skowron. "Approximation logic". In W. Bibel and K.P. Jantke, editors, Proceedings of the International Spring School, Mathematical Methods of Specification and Synthesis of Software Systems, LNCS 215. Springer-Verlag, 1985.
40. L. Polkowski, A. Skowron, and J. Zytkow. "Tolerance based rough sets". In T.Y. Lin and A.M. Wildberger, editors, Soft Computing, pages 55-58, 1995.
41. T.Y. Lin and Y.Y. Yao. "Neighborhoods systems: measure, probability and belief functions". In Proceedings of the 4th International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, pages 202-207, Tokyo, November 1996.
42. W. Sierpiński and C. Krieger. General Topology. University of Toranto Press, 1956.
43. W. Ziarko. "Variable precision rough set model". Journal of Computer and System Science, 46:39-59, 1993.
44. J.D. Katzberg and W. Ziarko. "Variable precision extension of rough set". Fundamenta Informaticae, 27:155-168, 1996.
45. D. Dubois and H. Prade. "Rough fuzzy sets and fuzzy rough sets". International Journal of General Systems, 17:191-200, 1990.
46. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, 1976.
47. A. Skowron. "Boolean reasoning for decision rules generation". In J.Komorowski and Z. W. Raś, editors, Proceedings of the 7th ISMIS, LNAI 689, pages 295-305. Springer-Verlag, 1993.
48. A. Skowron and J. W. Grzymala-Busse. "From rough set theory to evidence theory". In R. R. Yager, M. Federizzi, and J. Kacprzyk, editors, Advances in the Dempster-Shafer Theory of Evidence, pages 193-236. John Wiley and Sons, 1994.
49. C.J. Liau. "On the relationship between evidential structures and data tables". In M. De Glas and Z. Pawlak, editors, Proceedings of the 2nd World Conference on the Fundamentals of Artificial Intelligence, pages 205-216. Angkor, France, 1995.
50. S.K.M. Wong, L.S. Wang, and Y.Y. Yao. "Interval structure: a framework for representing uncertain information". In Proceedings of the 8th International Conference on Uncertainty in Artificial Intelligence, pages 336-343, 1993.
51. S.K.M. Wong, Y.Y. Yao, and L.S. Wang. "An application of rough sets in knowledge synthesis". In K. S. Harber, editor, Proceedings of the 7th ISMIS(Poster Session), ORNL/TM-12375, pages 140-150. Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, 1993.
52. R. Bull and K. Segerberg. "Basic modal logic". In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol II: Extensions of Classical Logic, pages 1-88. D. Reidel Publishing Company, 1984.
53. R.F. Fagin, J.Y. Halpern, Y. Moses, and M.Y. Vardi. Reasoning about Knowledge. MIT Press, 1996.
54. J.Y. Halpern and Y. Moses. "Knowledge and common knowledge in a distributed environment". JACM, 37(3):549-587, 1990.
55. N. Nilsson. "Probabilistic logic". Artificial Intelligence, 28:71-87, 1986.
56. R.F. Fagin and J.Y. Halpern. "Reasoning about knowledge and probability". In Proceedings of the 2th Conference on Theoretical Aspects of Reasoning about Knowledge, pages 277-293, 1988.
57. R.F. Fagin and J.Y. Halpern. "Uncertainty, belief , and probability". In Proceedings IJCAI-89, pages 1161-1167, 1989.
58. R.F. Fagin, J.Y. Halpern, and N. Megiddo. "A logic for reasoning about probabilities". Information and Computation, 87:78-128, 1990.
59. J.Y. Halpern. "An analysis of first-order logics of probability". Artificial Intelligence, 46:311-350, 1990.
60. W. van der Hoek. Modalities for Reasoning about Knowledge and Quantities. PhD thesis, Free University Amsterdam, 1992.
61. R.J. Aumann. "Agreeing to disagree". The Annals of Statistics, 4(6):1236-1239, 1976.
62. M. Fitting. "Many-valued modal logics". Fundamenta Informaticae, 15:235-254, 1992.
63. M. Fitting. "Many-valued modal logics II". Fundamenta Informaticae, 17:55-73, 1992.
64. J. Jaspars and E. Thijsse. "Fundamentals of partial modal logic". In P. Doherty, editor, Partiality, Modality, and Nonmonotonicity, pages 111-141. CSLI Publications, 1996.
65. P. Ostermann. "Many-valued modal propositional calculi". Zeitschrift f. Math. Logik und Grundlagen der Math, 34:343-354, 1988.
66. L. Godo and R. Rodriguez. "A similarity-based fuzzy modal logic". Submitted, 1998.
67. P. Hájek and D. Harmancová. "A many-valued modal logic". In Proceedings of IPMU'96, pages 1021-1024, 1996.
68. R.K. Schotch. "Fuzzy modal logic". In Proceedings of the 5th IEEE International Symposium on Mu;tiple-Valued Logic, pages 176-182, 1975.
69. H. Thiele. "On the definition of modal operators in fuzzy logic". In Proceedings of the 23rd IEEE International Symposium on Multiple-Valued Logic, pages 62-67, 1993.
70. D. M. Gabbay. "Fibring and labelling: Two methods for making modal logic fuzzy". In Proceedings of IFSA'97, pages 3-12, 1997.
71. C.J. Liau and I.P. Lin. "Quantitative modal logic and possibilistic reasoning". In B. Neumann, editor, Proceedings of the 10th ECAI, pages 43-47. John Wiley & Sons. Ltd, 1992.
72. C. J. Liau and I.P. Lin. "Reasoning about higher order uncertainty in possibilistic logic". In J. Komorowski and Z.W. Raś, editors, Proc. of 7th International Symposium on Methodologies for Intelligent Systems, LNAI 689, pages 316-325. Springer-Verlag, 1993.
73. C.J. Liau and I.P. Lin. "A theoretical investigation into quantitative modal logic". Fuzzy Sets and Systems, 75:355-363, 1995.
74. C.J. Liau and I.P. Lin. "Possibilistic Reasoning - A Mini-survey and Uniform Semantics". Artificial Intelligence, 88:163-193, 1996.
75. D. Dubois, F. Esteva, P. Garcia, L. Godo, and H. Prade. "Similarity-based consequence relations". In C. Froidevaux and J. Kohlas, editors, Symbolic and Quantitative Approaches to Uncertainty, LNAI 946, pages 168-174. Springer-Verlag, 1995.
76. F. Esteva, P. Garcia, L. Godo, and R. Rodriguez. "A modal account of similarity-based reasoning". International Journal of Approximate Reasoning, 16:235-260, 1997.
77. A. Nakamura. "Applications of fuzzy-rough classifications to logics". In R. Słowiński, editor, Intelligent Decison Support - Handbook of Applications and Advances of the Rough Set Theory, pages 233-250. Kluwer Academic Publishers, 1992.
78. A. Nakamura and J.M. Gao. "On a KTB-modal fuzzy logic". Fuzzy Sets and Systems, 45:327-334, 1992.
79. A. Nakamura. "Graded modalities in rough logic". In L. Polkowski and A. Skowron, editors, Rough Sets in Knowledge Discovery 1: Methodology and Applications, pages 192-208. Physica-Verlag, Heidelberg, Germany, 1998.
80. D. Dubois and H. Prade. "An introduction to possibilistic and fuzzy logics". In P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors, Non-Standard Logics for Automated Reasoning, pages 253-286. Academic Press, 1988.
81. Z. Pawlak. "Communication logic". Bulletin of Polish Academy of Sciences: Technical Science, 36:107-111, 1988.
82. W. Buszkowski. "Communication logic is an elementary theory". Bulletin of Polish Academy of Sciences: Mathematics, 35:637-642, 1987.
83. W. Buszkowski. "Second-order communication logic". Bulletin of Polish Academy of Sciences: Mathematics, 36:87-92, 1988.
84. A. Tzouvaras. "If the liar is intentional then his paradox can be resolved (Abstract)". In Proceedings of the 10th International Congress of Logic, Methodology and Philosophy of Science, page 182, 1995.
85. R. Montague. "Logical necessity, physical necessity, ethics, and quantifiers". Inquiry, 4:259-269, 1960.
86. J. Van Benthem. "Modal foundations for predicate logic". Logic Journal of the IGPL, 5(2):259-286, 1997.
87. J.H. Gallier. Logic for Computer Science. Harper & Row, Publishers, Inc., 1986.
88. + -valued logic". In Proceedings of the 16th IEEE International Symposium on Multiple-Valued Logic, pages 282-288, 1986.
89. M. Krynicki, M. Mostowski, and L.W. Szczerba. Quantifiers : Logics, Models, and Computation. Kluwer Academic Publishers, 1995.
90. K. Schlechta. "A reduction of the theory of confirmation to the notions of distance and measure". Logic Journal of the IGPL, 5(1):49-64, 1997.
91. D. Vakarelov. "Consequence relations and information systems". In R. Slowinski, editor, Intelligent Decision Support: Handbook of Applications and Advances of Rough Set Theory, pages 391-399. Kluwer Academic Publishers, 1992.
92. D. Vakarelov. "A duality between Pawlak's information systems and bi-consequence systems with applications to first-order and modal characterizations of some informational relations". In M. De Glas and Z. Pawlak, editors, Proceedings of the 2nd World Conference on the Fundamentals of Artificial Intelligence, pages 417-428. Angkor, France, 1995.
93. P. Pagliani. "A modal relation algebra for generalized approximation space". In S. Tsumoto, S. Kobayashi, T. Yokomori, H. Tanaka, and A. Nakamura, editors, Proceedings of the 2nd the 4th International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, pages 89-93. The University of Tokyo, 1996.
94. P. Pagliani. "A practical introduction to the modal-relational approach to approximation spaces". In L. Polkowski and A. Skowron, editors. Rough Sets in Knowledge Discovery 1: Methodology and Applications, pages 209-232. Physica-Verlag, Heidelberg, Germany, 1998.