Reasoning With Non-Binary Logics
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Reasoning With Non-Binary Logics

Authors: Sylvia Encheva

Abstract:

Students in high education are presented with new terms and concepts in nearly every lecture they attend. Many of them prefer Web-based self-tests for evaluation of their concepts understanding since they can use those tests independently of tutors- working hours and thus avoid the necessity of being in a particular place at a particular time. There is a large number of multiple-choice tests in almost every subject designed to contribute to higher level learning or discover misconceptions. Every single test provides immediate feedback to a student about the outcome of that test. In some cases a supporting system displays an overall score in case a test is taken several times by a student. What we still find missing is how to secure delivering of personalized feedback to a user while taking into consideration the user-s progress. The present work is motivated to throw some light on that question.

Keywords: Clustering, rough sets, many valued logic, predictions

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061148

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References:


[1] Avron, A. and Konikowska, B.: Rough Sets and 3-Valued Logics, Studia Logica, 90(1), (2008) 69-92
[2] Avron, A. and Lev,I.: Non-deterministic Multiple-valued Structures, Journal of Logic and Computation, 15, (2005) 241-261
[3] Bellman, R. E. and Zadeh, L. A., Decision making in a fuzzy environment, Management Sciences, Series B, 17, (1970), 141-164
[4] Belnap, N.J.: How a computer should think. In Contemporary Aspects of Philosophy. Proceedings of the Oxford International Symposia, Oxford, GB, (1975) 30-56
[5] Belnap, N.J.: A useful four.valued logic, Modern uses of multiplevalued logic, J.M. Dunn and G. Epstain (eds), D. Reidel Publishing Co., Dordrecht (1977) 8-37
[6] Bergmann, M.: An introduction to many-valued and fuzzy logic: semantics, algebras, and derivation systems. Cambridge University Press. (2008)
[7] Carlsson, C. and Fuller, R.: Optimization under the fuzzy if-then rules, Fuzzy Sets and Systems, 119(1), (2001)
[8] Carpineto, C. and Romano, G., Concept Data Analysis: Theory and Applications, John Wiley and Sons, Ltd., (2004)
[9] Davey, B. A., and Priestley, H.A.: Introduction to lattices and order. Cambridge University Press, Cambridge, (2005)
[10] Deng, J.L. Control problems of grey systems, System and control letters, 5, 1982, 288-294.
[11] Deng, J.L. Introduction to grey system theory, Journal of grey systems, 1, 1989, 1-24
[12] Fuller, R. and Zimmermann, H.-J.: Fuzzy reasoning for solving fuzzy mathematical programming problems, Fuzzy Sets and Systems 60, 121-133 (1993)
[13] Goodstein, R. L.: Boolean Algebra. Dover Publications, 2007
[14] E. Gradel, M. Otto, and E. Rosen, Undecidability results on twovariable logics, Archive of Mathematical Logic, vol. 38, 1999, pp. 313-354
[15] Guzm`an, E., Conejo, R.: A model for student knowledge diagnosis through adaptive testing. Lecture Notes in Computer Science, 3220, Springer-Verlag, Berlin Heidelberg New York, 2004, 12-21
[16] D. M. Harris and S. L. Harris. Digital Design and Computer Architecture. Morgan Kaufmann, 2007.
[17] Herrmann, C. S.: Fuzzy logic as inferencing techniques in hybrid AISystems, Lecture Notes in Computer Science 1188, 69–80 (1997)
[18] Y.C. Hu, Grey relational analysis and radical basis function network for determining costs in learning sequences, Applied mathematics and computation, 184, 2007, 291-299.
[19] Huffman, D, Goldberg, F., Michlin, M.: Using computers to create constructivist environments: impact on pedagogy and achievement. Journal of Computers in mathematics and science teaching, 22(2), 2003, 151–168
[20] N. Immerman, A. Rabinovich, T. Reps, M. Sagiv, and G. Yorsh, The boundery between decidability and undecidability of transitive closure logics, In: CSL’04, 2004
[21] Kaluzhny Y., Muravitsky A.Y.: A knowledge representation based on the Belnap’s four valued logic, Journal of Applied Non-Classical Logics, 3, (1993) 189–203
[22] Z. Kurmas, Improving Student Performance Using Automated Testing of Simulated Digital Logic Circuits, ITiCSE08, June 30-July 2, 2008, Madrid, Spain.
[23] Lei, Y., Wang, Y., Cao B. and Yu J.: Concept Interconnection Based on Many-Valued Context Analysis, Lecture Notes in Computer Science, 4426, 623–630, 2007
[24] Liu J. and Yao, X.: Formal concept analysis of incomplete information system, Seventh International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2016 – 2020, 2010
[25] Malinowski G.: Many-valued logics. Clarendon Press, (1993)
[26] Park, C., Kim, M.: Development of a Level-Based Instruction Model in Web-Based Education. Lecture Notes in Artificial Intelligence, 3190. Springer-Verlag, Berlin Heidelberg New York, 2003, 215–221
[27] Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences, 11, (1982) 341–356
[28] Z. Pawlak. Rough Sets: Theoretical Aspects of Reasoning about Data, vol. 9 Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
[29] L. Polkowski and A. Skowron. Rough mereological approach to knowledge-based distributed AI. pages 774781, Soeul, Korea, February 5-9 1996.
[30] L. Polkowski and A. Skowron. Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning, 15(4):333- 365, 1996.
[31] L. Polkowski and A. Skowron. Rough mereology in information systems. A case study: Qualitative spatial reasoning. vol. 56 pages 89135. Springer-Verlag/Physica- Verlag, Heidelberg, Germany, 2000.
[32] F. Rahimnia, M. Moghadasian and E. Mashreghi, Application of grey theory organizational approach to evaluation of organizational vision, Grey Systems: Theory and Application, vol. 1 No. 1, 2011, 33-46
[33] Whitesitt, J.E.: Boolean Algebra and Its Applications, Dover Publications, 1995
[34] R. Wille, Concept lattices and conceptual knowledge systems, Computers Math. Applications, vol. 23(6-9), 1992, pp. 493-515
[35] Zadeh, L. A., The concept of linguistic variable and its applications to approximate reasoning, Parts I, II, III, Information Sciences, 8(1975) 199-251; 8(1975) 301-357; 9(1975) 43-80.