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Measure-Based Semantics for Modal Logic

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Fuzzy Logic

Part of the book series: Theory and Decision Library ((TDLD,volume 12))

Abstract

A fuzzy-measure-based approach to semantics for modal logic is presented and its several properties are discussed. Measure-based models for modal logic are defined and the soundness and completeness theorems of several systems of modal logic are proved with respect to classes of finite measure-based models, particularly, formulated by fuzzy, possibility, necessity, probability, and Dirac measures.

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References

  1. B.F. Chellas, Modal Logic: An Introduction. Cambridge University Press, 1980.

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  2. D. Dubois and H. Prade, A Class of Fuzzy Measures Based on Triangular Norms. International Journal of General Systems, 8(1982), 43–61.

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  3. S. Miyamoto, Fuzzy Sets in Information Retrieval and Cluster Analysis. Kluwer Academic Publishers, 1990.

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  4. T. Murai, M. Miyakoshi, and M. Shimbo, Modeling of Indexing in Document Retrieval Based on Doxastic Modal Operators Defined by Fuzzy Measures. Proceedings of the Second International Conference on Fuzzy Logic and Neural Networks (IIZUKA’ 92), to appear.

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  5. T. Murai, M. Miyakoshi, and M. Shimbo, Multi-Modal Logic of Belief Based on the Dempster-Shafer Theory, in manuscript.

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  6. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, 1976.

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  7. P. Smets, A. Mamdani, D. Dubois, and H. Prade (eds.), Non-Standard Logics for Automated Reasoning, Academic Press, 1988.

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© 1993 Springer Science+Business Media Dordrecht

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Murai, T., Miyakoshi, M., Shimbo, M. (1993). Measure-Based Semantics for Modal Logic. In: Lowen, R., Roubens, M. (eds) Fuzzy Logic. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2014-2_37

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  • DOI: https://doi.org/10.1007/978-94-011-2014-2_37

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4890-3

  • Online ISBN: 978-94-011-2014-2

  • eBook Packages: Springer Book Archive

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