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Paraconsistency, Chellas’s Conditional Logics, and Association Rules

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Towards Paraconsistent Engineering

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 110))

Abstract

Paraconsistency and its dual paracompleteness are now counted as key concepts in intelligent decision systems because so much inconsistent and incomplete information can be found around us. In this paper, a framework of conditional models for conditional logic and their measure-based extensions are introduced in order to represent association rules in a logical way. Then paracomplete and paraconsistent aspects of conditionals are examined in the framework. Finally we apply conditionals into the definition of association rules in data mining with confidence and consider their extension to the case of Dempster-Shaer theory of evidence serving double-indexed confidence.

Dedicated to Jair Minoro Abe for his 60th birthday

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Notes

  1. 1.

    In [7], Chellas used only \({{\Box }\!\rightarrow }\). The latter connective \({{\Diamond }\!\rightarrow }\) follows Lewis [11].

References

  1. Agrawal, R., Imielinski, T., Swami, A.: Mining association rules between sets of items in large databases. In: Proceedings of the ACM SIGMOD Conference on Management of Data, pp. 207–216 (1993)

    Google Scholar 

  2. Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast discovery of association rules. In: Fayyad, U.M., Platetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.) Advances in Knowledge Discovery and Data Mining, pp. 307–328. AAAI Press/The MIT Press (1996)

    Google Scholar 

  3. Aggarwal, C.C., Philip, S.Y.: Online generation of association rules. In: Proceedings of the International Conference on Data Engineering, pp. 402–411 (1998)

    Google Scholar 

  4. Akama, S., Abe, J.M.: Many-valued and annotated modal logics. In: Proceedings of 28th ISMVL, pp. 114–119 (1998)

    Google Scholar 

  5. Akama, S., Abe, J.M.: Fuzzy annotated logics. In: Proceedings of IPMU 2000, pp. 504–509 (2000)

    Google Scholar 

  6. Akama, S., Abe, J.M.: Paraconsistent logics viewed as a foundation of data warehouses. Advances in Logic, Artificial Intelligence and Robotics, pp. 96–103. IOS Press (2002)

    Google Scholar 

  7. Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)

    Google Scholar 

  8. da Costa, N.C.A., Abe, J.M., Subrahmanian, V.S.: Remarks on annotated logic. Zeitschr. f. Math. Logik und Grundlagen d. Math. 37, 561–570 (1991)

    Google Scholar 

  9. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Springer (1988)

    Google Scholar 

  11. Lewis, D.: Counterfactuals. Blackwell, Oxford (1973)

    MATH  Google Scholar 

  12. Murai, T., Miyakoshi, M., Shimbo, M.: Measure-based semantics for modal logic. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic: State of the Art, pp. 395–405. Kluwer, Dordrecht (1993)

    Google Scholar 

  13. Murai, T., Miyakoshi, M., Shimbo, M.: Soundness and completeness theorems between the Dempster-Shafer theory and logic of belief. In: Proceedings of the 3rd FUZZ-IEEE (WCCI), pp. 855–858 (1994)

    Google Scholar 

  14. Murai, T., Miyakoshi, M., Shimbo, M.: A logical foundation of graded modal operators defined by fuzzy measures. In: Proceedings of the 4th FUZZ-IEEE/2nd IFES, pp. 151–156 (1995)

    Google Scholar 

  15. Murai, T., Sato, Y.: Association rules from a point of view of modal logic and rough sets. In: Proceedings of the 4th AFSS, pp. 427–432 (2000)

    Google Scholar 

  16. Murai, T., Nakata, M., Sato, Y.: A note on conditional logic and association rules. In: Terano, T., et al. (eds.) New Frontiers in Artificial Intelligence, LNAI, vol. 2253, pp. 390–394. Springer (2001)

    Google Scholar 

  17. Murai, T., Nakata, M., Sato, Y.: Association rules as relative modal sentences based on conditional probability. Commun. Inst. Inf. Comput. Mach. 5(2), 73–76 (2002)

    Google Scholar 

  18. Murai, T., Sato, Y., Kudo, Y.: Paraconsistency and neighborhood models in modal logic. In: Proceedings of the 7th World Multiconference on Systemics, Cybernetics and Informatics, vol. XII, pp. 220–223 (2003)

    Google Scholar 

  19. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)

    Google Scholar 

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Acknowledgments

We are grateful to a referee for useful comments.

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Authors and Affiliations

  1. Chitose Institute of Science and Technology, Chitose, 066-8655, Japan

    Tetsuya Murai

  2. Muroran Institute of Technology, Muroran, Japan

    Yasuo Kudo

  3. C-Republic, 1-20-1 Higashi-Yurigaoka, Asao-ku, Kawasaki, 215-0012, Japan

    Seiki Akama

Authors
  1. Tetsuya Murai
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  2. Yasuo Kudo
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  3. Seiki Akama
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Correspondence to Tetsuya Murai .

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Editors and Affiliations

  1. Kawasaki, Japan

    Seiki Akama

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Murai, T., Kudo, Y., Akama, S. (2016). Paraconsistency, Chellas’s Conditional Logics, and Association Rules. In: Akama, S. (eds) Towards Paraconsistent Engineering. Intelligent Systems Reference Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-40418-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-40418-9_9

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