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Conjunction of Conditional Events and t-Norms

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11726))

Abstract

We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t-norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm.

A. Gilio and G. Sanfilippo—Both authors contributed equally to the article and are listed alphabetically.

A. Gilio—Retired.

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Acknowledgments

We thank three anonymous referees for their useful comments.

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Authors and Affiliations

  1. Department SBAI, University of Rome “La Sapienza”, Rome, Italy

    Angelo Gilio

  2. Department of Mathematics and Computer Science, University of Palermo, Palermo, Italy

    Giuseppe Sanfilippo

Authors
  1. Angelo Gilio
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  2. Giuseppe Sanfilippo
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Corresponding authors

Correspondence to Angelo Gilio or Giuseppe Sanfilippo .

Editor information

Editors and Affiliations

  1. Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Zoran Ognjanović

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Gilio, A., Sanfilippo, G. (2019). Conjunction of Conditional Events and t-Norms. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_17

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  • DOI: https://doi.org/10.1007/978-3-030-29765-7_17

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