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On Independence and Compound and Iterated Conditionals

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Human and Artificial Rationalities (HAR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14522))

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Abstract

Understanding the logic of uncertain conditionals is a key problem in the new paradigm psychology of reasoning and related fields. We investigate conjunctions of conditionals, iterated conditionals, and independence within the theory of logical operations on conditionals, where compound conditionals are suitably defined as conditional random quantities. We show how conjunctions of conditionals and conditionals which feature conditionals in the antecedent and the consequent can be rationally interpreted. In particular, we study the behavior of such objects under different logical constraints, by also considering a kind of “independence” property. Unlike alternative approaches, in our framework we avoid counterintuitive consequences, which is necessary for understanding, or improving, human and artificial rationality in general.

A. Gilio—Retired.

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Acknowledgements

We thank three anonymous reviewers, John Cantwell, and the chair for useful comments and suggestions. G. Sanfilippo is member of the INdAM-GNAMPA research group and is supported by the FFR 2024 project of University of Palermo, Italy.

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Authors and Affiliations

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

    Angelo Gilio

  2. Department of Psychology, Durham University, Durham, UK

    David Over

  3. Department of Philosophy, University of Regensburg, Regensburg, Germany

    Niki Pfeifer

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

    Giuseppe Sanfilippo

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  1. Angelo Gilio
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  2. David Over
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  3. Niki Pfeifer
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  4. Giuseppe Sanfilippo
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Correspondence to Giuseppe Sanfilippo .

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Editors and Affiliations

  1. Université Paris 8, Saint Denis, France

    Jean Baratgin

  2. Université Paris 8, Saint-Denis, France

    Baptiste Jacquet

  3. Osaka City University, Osaka, Japan

    Hiroshi Yama

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Gilio, A., Over, D., Pfeifer, N., Sanfilippo, G. (2024). On Independence and Compound and Iterated Conditionals. In: Baratgin, J., Jacquet, B., Yama, H. (eds) Human and Artificial Rationalities. HAR 2023. Lecture Notes in Computer Science, vol 14522. Springer, Cham. https://doi.org/10.1007/978-3-031-55245-8_11

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  • DOI: https://doi.org/10.1007/978-3-031-55245-8_11

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