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Different Forms of Generalized Hypothetical Syllogism with Regard to R-Implications

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Artificial Intelligence and Soft Computing (ICAISC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11508))

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Abstract

In this paper we investigate the generalized hypothetical syllogism (GHS). We present few versions of the well known GHS equation. We focus our attention on R-implications and give some results concerning left-continuous t-norms. We show some solutions of GHS equations based on the compositional rule of inference and Bandler-Kohout subproduct. Also we sketch the idea of new possible functional equations coming from the GHS.

This work was supported by the National Science Centre, Poland, through research Project Number 2015/19/B/ST6/03259.

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Acknowledgment

This work was supported by the National Science Centre, Poland, through research Project Number 2015/19/B/ST6/03259. The authors would like to thank Professor Balasubramaniam Jayaram for the inspiring discussion during his stay in Katowice and his constructive suggestions which contributed to the development of this research topic.

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Authors and Affiliations

  1. Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland

    Katarzyna Miś & Michał Baczyński

Authors
  1. Katarzyna Miś
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  2. Michał Baczyński
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Corresponding author

Correspondence to Michał Baczyński .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

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Miś, K., Baczyński, M. (2019). Different Forms of Generalized Hypothetical Syllogism with Regard to R-Implications. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2019. Lecture Notes in Computer Science(), vol 11508. Springer, Cham. https://doi.org/10.1007/978-3-030-20912-4_29

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  • DOI: https://doi.org/10.1007/978-3-030-20912-4_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-20911-7

  • Online ISBN: 978-3-030-20912-4

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