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Conditional Objects as Possibilistic Variables

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14294))

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Abstract

The interpretation of basic conditionals as three-valued objects initiated by de Finetti has been mainly developed and extended by Gilio and Sanfilippo and colleagues, who look at (compound) conditionals as probabilistic random quantities. Recently, it has been shown that this approach ends up providing a Boolean algebraic structure for the set of conditional objects. In this paper, we show how that this probabilistic-based approach can also be developed within the possibilistic framework, where conditionals are attached with possibilistic variables instead: variables attached with a (conditional) possibility distribution on its domain of plain events. The possibilistic expectation of these variables now provides a means of extending the original possibility distribution on events to (compound) conditional objects. Our main result shows that this possibilistic approach leads to exactly the same underlying Boolean algebraic structure for the set of conditionals.

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Notes

  1. 1.

    Called T-conditional possibility in [9, 10].

  2. 2.

    This is a possibilistic counterpart of the formula given in [30] for the probability of the conjunction of two conditionals.

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Acknowledgments

The authors are thankful to the anonymous reviewers for their comments and suggestions. The authors also acknowledge support by the support by the MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627) and by the Spanish projects PID2019-111544GB-C21 and PID2022-139835NB-C21 funded by MCIN/AEI/10.13039/501100011033.

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Authors and Affiliations

  1. IIIA - CSIC, 08193, Bellaterra, Spain

    Tommaso Flaminio & Lluis Godo

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  1. Tommaso Flaminio
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  2. Lluis Godo
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Correspondence to Lluis Godo .

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Editors and Affiliations

  1. CRIL CNRS University Artois, Lens Cedex, France

    Zied Bouraoui

  2. CRIL CNRS University Artois, Lens Cedex, France

    Srdjan Vesic

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Flaminio, T., Godo, L. (2024). Conditional Objects as Possibilistic Variables. In: Bouraoui, Z., Vesic, S. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2023. Lecture Notes in Computer Science(), vol 14294. Springer, Cham. https://doi.org/10.1007/978-3-031-45608-4_28

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  • DOI: https://doi.org/10.1007/978-3-031-45608-4_28

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