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Characterizing Multipreference Closure with System W

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Scalable Uncertainty Management (SUM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13562))

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Abstract

System W is an approach to reasoning from conditional beliefs that exhibits many properties desirable for nonmonotonic reasoning like extending rational closure, avoiding the drowning problem, and complying with syntax splitting. Multipreference closure, initially considered for reasoning in description logics with exceptions, has recently been reconstructed as a method for reasoning with conditionals based on propositional logic by Giordano and Gliozzi; this reconstruction is rather involved and complex. In this paper, we show how system W can be used to obtain a significantly less involved semantical characterization of MP-closure. To do this, we first present a representation theorem for system W using a canonical preferential model \(\mathcal {M}^{\textsf {w}}(\varDelta )\) for a belief base \(\varDelta \) that is obtained straightforwardly from system W. We then prove our main result, stating that \(\mathcal {M}^{\textsf {w}}(\varDelta )\) also induces the MP-closure of \(\varDelta \); furthermore, this implies that MP-closure coincides with system W inference.

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Acknowledgements

We thank the anonymous reviewers for their detailed and helpful comments. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant BE 1700/10-1 awarded to Christoph Beierle as part of the priority program “Intentional Forgetting in Organizations” (SPP 1921).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, FernUniversität in Hagen, 58084, Hagen, Germany

    Jonas Haldimann & Christoph Beierle

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  1. Jonas Haldimann
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  2. Christoph Beierle
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Correspondence to Jonas Haldimann .

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Editors and Affiliations

  1. IRIT-Université Toulouse, Toulouse, France

    Florence Dupin de Saint-Cyr

  2. Université Paris-Dauphine - PSL, Paris, France

    Meltem Öztürk-Escoffier

  3. Imperial College London, London, UK

    Nico Potyka

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Haldimann, J., Beierle, C. (2022). Characterizing Multipreference Closure with System W. In: Dupin de Saint-Cyr, F., Öztürk-Escoffier, M., Potyka, N. (eds) Scalable Uncertainty Management. SUM 2022. Lecture Notes in Computer Science(), vol 13562. Springer, Cham. https://doi.org/10.1007/978-3-031-18843-5_6

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  • DOI: https://doi.org/10.1007/978-3-031-18843-5_6

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  • Print ISBN: 978-3-031-18842-8

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