×

An overview of rough set semantics for modal and quantifier logics. (English) Zbl 1113.03309

Summary: We would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some well-known results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.

MSC:

03B45 Modal logic (including the logic of norms)
03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Liau G.J., R. Trappl, editor, Proceedings of the 14th European Meeting on Cybernetics and Systems Research, pages pp 175– (1998)
[2] Liau G.J., Proceedings of the 8th International Conference on Artificial Intelligence: Methodology, Systems, Applications, pages 317 pp 1480– (1998)
[3] Pawlak Z., International ence 11 pp 341– (1982)
[4] Oriowska E., Studia Logica pp 93– (1985)
[5] Oriowska E., Bulletin of the Polish Academy of Science: Mathematics 33 pp 473– (1985)
[6] Oriowska E., Bulletin of the Polish Academy of Science: Mathematics 35 pp 255– (1987)
[7] Orlowska E., Bulletin Science: Mathematics 35 pp 643– (1987)
[8] DOI: 10.1002/malq.19890350612 · Zbl 0711.03008 · doi:10.1002/malq.19890350612
[9] DOI: 10.1007/BF00935602 · Zbl 0726.03023 · doi:10.1007/BF00935602
[10] DOI: 10.1016/0304-3975(85)90046-5 · Zbl 0565.68032 · doi:10.1016/0304-3975(85)90046-5
[11] C.M., J.Komorowski and Z. W. Ras, editors, Proceedings pages 326 (1993)
[12] Vakarelov D., A.R. Meyer and M.A. Taitslin, editors, Proceedings of Symposium on Logical Foundations of Computer Science, LNGS 363 pp 257– (1989)
[13] Konikowska B., Bulletin of the Polish Academy of Science: Mathematics 35 pp 239– (1987)
[14] DOI: 10.1080/10798587.1996.10750660 · doi:10.1080/10798587.1996.10750660
[15] DOI: 10.1016/S0888-613X(96)00071-0 · Zbl 0935.03063 · doi:10.1016/S0888-613X(96)00071-0
[16] Pawlak Z., Bulletin of the Polish Academy of Science 35 pp 253– (1987)
[17] DOI: 10.1002/malq.19900360109 · Zbl 0712.03025 · doi:10.1002/malq.19900360109
[18] DOI: 10.2307/2274702 · Zbl 0736.03011 · doi:10.2307/2274702
[19] Szczerba L.W., Bulletin Mathematics 35 pp 251– (1987)
[20] LNGS 208 pp 288–
[21] Polkowski L., T.Y. Lin and A.M. Wildberger, editors, Soft Computing, pages pp 55– (1995)
[22] DOI: 10.1016/0022-0000(93)90048-2 · Zbl 0764.68162 · doi:10.1016/0022-0000(93)90048-2
[23] Katzberg J.D., Fundamenta Informaticae 27 pp 155– (1996)
[24] Dubois D., International Journal of General Systems
[25] Skowron A., J.Kornorowski and Z. W. Ras, editors, Proceedings of the 7th ISMIS, LNA1689, pages 295 (1993)
[26] Skowron A., R. R. Yager, M. Federizzi, and J. Kacprzyk, editors, Advances in the Dempster-Shafer Theory of Evidence, pages 193
[27] Wong K.M., Proceedings of the 8th International Conference on Uncertainty in Artificial Intelligence, pages pp 336– (1993)
[28] DOI: 10.1145/79147.79161 · Zbl 0699.68115 · doi:10.1145/79147.79161
[29] DOI: 10.1016/0004-3702(86)90031-7 · Zbl 0589.03007 · doi:10.1016/0004-3702(86)90031-7
[30] Fagin R.F., Proceedings of the 2th Conference on Theoretical Aspects of Reasoning about Knowledge, pages pp 277– (1988)
[31] Fagin R.F., Proceedings IJCAI-89, pages pp 1161– (1989)
[32] DOI: 10.1016/0890-5401(90)90060-U · Zbl 0811.03014 · doi:10.1016/0890-5401(90)90060-U
[33] DOI: 10.1016/0004-3702(90)90019-V · Zbl 0723.03007 · doi:10.1016/0004-3702(90)90019-V
[34] DOI: 10.1214/aos/1176343654 · Zbl 0379.62003 · doi:10.1214/aos/1176343654
[35] Fitting M., Fundamenta Informaticae 15 pp 235– (1992)
[36] Fitting M., Fundamenta Informaticae 17 pp 55– (1992)
[37] DOI: 10.1002/malq.19880340411 · Zbl 0661.03011 · doi:10.1002/malq.19880340411
[38] Schotch P.K., Proceedings of the 5th IEEE International Symposium on Mu;tiple-Valued Logic, pages pp 176– (1975)
[39] Liau C.J., J. Komorowski and Z.W. Ras, editors, Proc. of 7th International Symposium on Methodologies for Intelligent Systems, LNAI 689 pp 316– (1993)
[40] DOI: 10.1016/0165-0114(95)00006-7 · Zbl 0853.03003 · doi:10.1016/0165-0114(95)00006-7
[41] DOI: 10.1016/S0004-3702(96)00013-6 · Zbl 0907.68180 · doi:10.1016/S0004-3702(96)00013-6
[42] Dubois D., C. Froidevaux and J. Kohlas, editors, Symbolic and Quantitative Approaches to Uncertainty, LNAI 946 pp 168– (1995)
[43] DOI: 10.1016/S0888-613X(96)00126-0 · Zbl 0935.03037 · doi:10.1016/S0888-613X(96)00126-0
[44] DOI: 10.1016/0165-0114(92)90151-S · Zbl 0754.03014 · doi:10.1016/0165-0114(92)90151-S
[45] Buszkowski W., Bulletin of Polish Academy of Sciences: Mathematics 35 pp 637– (1987)
[46] Buszkowski W., Bulletin Sciences: Mathematics 36 pp 87– (1988)
[47] Tzouvaras A., . In Proceedings of the 10th International Philosophy of Science, page pp 182– (1995)
[48] DOI: 10.1080/00201746008601312 · doi:10.1080/00201746008601312
[49] DOI: 10.1093/jigpal/5.2.259 · Zbl 0949.03517 · doi:10.1093/jigpal/5.2.259
[50] Rasiowa H., Proceedings of the 16th IEEE International Symposium on Multiple- Valued Logic, pages pp 282– (1986)
[51] DOI: 10.1093/jigpal/5.1.49 · Zbl 0872.03014 · doi:10.1093/jigpal/5.1.49
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.