Abstract
In order to distinguish and deal with different negations of fuzzy knowledge, we have presented a fuzzy propositional logic with contradictory negation, opposite negation, medium negation, FScom for short. In this paper, we further study semantics of FLcom. Based on the three-value interpretation of FLcom, the soundness theorem and completeness theorem for FLcom are proved.
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References
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1996)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)
Wagner, G.: Web Rules Need Two Kinds of Negation. Lecture Notes in Computer Science, vol. 2901. Springer, Berlin (2003)
Analyti, A., Antoniou, G., Wagner, G., et al.: Negation and negative information in the W3C resource description framework. Ann. Math., Comput. Teleinf. 1(2), 25–34 (2004)
Dung, P.M., Mancarella, P.: Production systems need negation as failure. IEEE Trans. Knowl. Data Eng. 14(2), 336–353 (2002)
Ferré, S.: Negation, Opposition, and Possibility in Logical Concept Analysis. Lecture Notes in Artificial intelligence, vol. 3874, pp. 130–145. Springer, Berlin (2006)
Kaneiwa, K.: Negations in description logic with contraries, contradictories, and subcontraries. New Gener. Comput. 25(4): 443–468
Pan, Z.H., Zhu, W.J.: A new cognition and processing on contradictory knowledge. In: Proceedings of the IEEE-International Conference on Machine Learning and Cybernetics, vol. 3, pp. 1532–1537. IEEE-Computer Society, Washington (2006)
Pan, Z.H., Zhang, S.L.: Differentiation and processing on contradictory relation and opposite relation in knowledge. In: Proceedings of the IEEE-Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), vol. 4, pp. 334–3389. IEEE-Computer Society, Washington (2007)
Pan, Z.H., Wang, C., Zhang, L.J.: Three kinds of negations of fuzzy knowledge and applications to decision making in financial investment. Lecture Notes in Artificial Intelligence, vol. 6422, pp. 391–401. Springer, Berlin (2010)
Pan, Z.H.: Fuzzy set with three kinds of negation and its applications in fuzzy decision making. Lecture Notes in Artificial Intelligence, vol. 7002, pp. 533–542. Springer, Berlin (2011)
Pan, Z.H.: Fuzzy propositional logic system of distinguish between three kinds of negation and its application. J. Softw. 25(6), 1255–1272 (2014)
Acknowledgments
This work is supported by the National Natural Science Foundation of China (61375004) and the Fundamental Research Funds for the Central Universities (JUSRP51317B).
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Pan, ZH. (2017). Soundness and Completeness of Fuzzy Propositional Logic with Three Kinds of Negation. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_8
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DOI: https://doi.org/10.1007/978-3-319-46206-6_8
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