Paraconsistent Logic with Multiple Fuzzy Linguistic Truth-values

Manren Wang, Xudong Luo

Abstract

This paper extends the two-valued paraconsistent logic into an one in which a proposition takes a truth-value from a set of multiple fuzzy linguistic terms. More specifically, we propose the corresponding inference rule and semantics, and finally prove the soundness of our new fuzzy logical system and its completeness. Moreover, we use an example to illustrate the applicability of our logic system in real life.

References

  1. Abe, J. M. (2016). Paraconsistent logics and applications. In New Approaches in Intelligent Control, volume 107 of Intelligent Systems Reference Library, pages 273- 300. Springer.
  2. Akama, S. and Da Costa, N. C. (2016). Why paraconsistent logics? In Towards Paraconsistent Engineering, volume 110 of Intelligent Systems Reference Library, pages 7-24. Springer.
  3. Anderson, A. R., Belnap, N. D., and Dunn, J. M. (1978). Entailment: The logic of relevance and necessity. Philosophical Books, 19(2):75-77.
  4. Arnon, A. (2014). Paraconsistent fuzzy logic preserving non-falsity. Fuzzy Sets and Systems, 292:75-84.
  5. Costa, N. D. and Carnielli, W. (1986). On paraconsistent deontic logic. Philosophia, 16(3-4):293-305.
  6. Costa, N. D., D.Krause, and O.Bueno (2005). Paraconsistent logics and paraconsistency. Philosophy of Logic, 4:791-911.
  7. Da Costa, N. C., Béziau, J.-Y., Bueno, O. A., et al. (1995). Aspects of paraconsistent logic. Logic Journal of the IGPL, 3(4):597-614.
  8. Da Costa, N. C. A. (1958). On the theory of inconsistent formal systems. Bulletin De La Socit De Chimie Biologique, 40(7-8):1179-1187.
  9. Dou, F., Jia, L., Wang, L., Xu, J., and Huang, Y. (2014). Fuzzy temporal logic based railway passenger flow forecast model. Computational Intelligence and Neuroscience, 2014:Article No. 42.
  10. Ertola, R., Esteva, F., Flaminio, T., Godo, L., and Noguera, C. (2013). Exploring paraconsistency in degreepreserving fuzzy logics. In Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology, pages 117-124.
  11. Ijsselmuiden, J., Nch, D., Grosselfinger, A. K., Arens, M., and Stiefelhagen, R. (2014). Automatic understanding of group behavior using fuzzy temporal logic. Journal of Ambient Intelligence and Smart Environments, 6(6):623-649.
  12. Jing, X., Luo, X., and Zhang, Y. (2014). A fuzzy dynamic belief logic system. International Journal of Intelligent Systems, 29(7):687-711.
  13. Kamide, N. (2013). Formalizing inconsistency-tolerant relevant human reasoning: A decidable paraconsistent relevant logic with constructible falsity. In Proceedings of 2013 IEEE International Conference on Systems, Man, and Cybernetics, pages 1865-1870.
  14. Kamide, N. (2016). A decidable paraconsistent relevant logic: Gentzen system and routley-meyer semantics. Mathematical Logic Quarterly, 62(3):177-189.
  15. Moon, S., Lee, K., and Lee, D. (2004). Fuzzy branching temporal logic. IEEE Transactions on Systems Man and Cybernetics: Part B Cybernetics, 34(2):1045- 1055.
  16. Mukherjee, S. and Dasgupta, P. (2013). A fuzzy real-time temporal logic. International Journal of Approximate Reasoning, 54(9):1452-1470.
  17. Poli, V. S. R. (2015). Fuzzy temporal predicate logic for incomplete information. In Proceedings of 2015 International Conference on Fuzzy Theory and Its Applications, pages 86-90.
  18. Priest, G., Tanaka, K., and Weber, Z. (1989). Paraconsistent Logic. München.
  19. Rodrguez, J., Turunen, E., Da, R., and Montero, J. (2014). Another paraconsistent algebraic semantics for lukasiewiczpavelka logic. Fuzzy Sets and Systems, 242(242):132-147.
  20. Tanaka, K., Berto, F., Mares, E., and Paoli, F. (2012). Paraconsistency: Logic and applications, volume 26. Springer.
  21. Thiele, H. and Kalenka, S. (1993). On fuzzy temporal logic. In Proceeding of the 2nd IEEE International Conference on Fuzzy Systems, pages 1027-1032.
  22. Turunen, E. (1992). On fuzzy intuitionistic logic. Kybernetika, 28(7):72-77.
  23. Turunen, E., Oztürk, M., and Tsoukis, A. (2010). Paraconsistent semantics for pavelka style fuzzy sentential logic. Fuzzy Sets and Systems, 161(14):1926-1940.
  24. Vidal, A., Esteva, F., and Godo, L. (2015). On modal extensions of product fuzzy logic. Journal of Logic and Computation, page exv046.
  25. Yager, R. R. and Zadeh, L. A. (1992). An Introduction to Fuzzy Logic Applications in Intelligent systems, volume 165 of The International Series in Engineering and Computer Science. Springer.
  26. Yang, W. (2005). Theoretical significance and practical value of paraconsistent logic. Journal of Renmin University of China, (2):63-69.
  27. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(65):338-353.
  28. Zadeh, L. A. (1983). The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy sets and systems, 11(1):199-227.
  29. Zadeh, L. A. (1996). Fuzzy logic=computing with words. IEEE transactions on fuzzy systems, 4(2):103-111.
  30. Zhan, J., Luo, X., Feng, C., and Ma, W. (2014). A fuzzy logic based bargaining model in discrete domains: Axiom, elicitation and property. In Proceedings of 2014 IEEE International Conference on Fuzzy Systems, pages 424-431.
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Paper Citation


in Harvard Style

Wang M. and Luo X. (2017). Paraconsistent Logic with Multiple Fuzzy Linguistic Truth-values . In Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-220-2, pages 53-62. DOI: 10.5220/0006117200530062


in Bibtex Style

@conference{icaart17,
author={Manren Wang and Xudong Luo},
title={Paraconsistent Logic with Multiple Fuzzy Linguistic Truth-values},
booktitle={Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2017},
pages={53-62},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006117200530062},
isbn={978-989-758-220-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Paraconsistent Logic with Multiple Fuzzy Linguistic Truth-values
SN - 978-989-758-220-2
AU - Wang M.
AU - Luo X.
PY - 2017
SP - 53
EP - 62
DO - 10.5220/0006117200530062