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Syntax Splitting for Iterated Contractions, Ignorations, and Revisions on Ranking Functions Using Selection Strategies

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Logics in Artificial Intelligence (JELIA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12678))

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Abstract

For characterizing belief sets consisting of independent parts, Parikh introduced the notion of syntax splitting. Corresponding postulates have been developed for the reasoning from and for the revision of belief bases with respect to syntax splitting. Kern-Isberner and Brewka introduced syntax splitting for epistemic states and iterated belief revision. Only recently, syntax splitting has also been studied for contractions and iterated contractions of epistemic states; however, all of the evaluated contractions proposed in the literature failed to fulfil the full syntax splitting postulates. In this paper, we study syntax splitting for iteratively contracting and revising epistemic states, represented by ranking functions, not only with respect to a set of formulas, but with respect to a set of conditionals. Using a framework of belief change governed by the principle of conditional preservation, we employ the concept of selection strategies. We develop axioms for selection strategies ensuring that the induced contractions and revisions fully obey the desired syntax splitting properties. Furthermore, we transfer our approach to ignorations and prove a theorem showing how selection strategies satisfying the axioms can effectively be constructed.

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Acknowledgements

We thank the anonymous reviewers for their valuable hints. This work was supported by DFG Grant BE 1700/9-1 awarded to Christoph Beierle and DFG Grant KE 1413/10-1 awarded to Gabriele Kern-Isberner as part of the priority program “Intentional Forgetting in Organizations” (SPP 1921).

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Authors and Affiliations

  1. FernUniversität in Hagen, 58084, Hagen, Germany

    Jonas Haldimann & Christoph Beierle

  2. TU Dortmund University, 44227, Dortmund, Germany

    Gabriele Kern-Isberner

Authors
  1. Jonas Haldimann
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  2. Christoph Beierle
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  3. Gabriele Kern-Isberner
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Correspondence to Jonas Haldimann .

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Editors and Affiliations

  1. University of Klagenfurt, Klagenfurt, Austria

    Wolfgang Faber

  2. University of Klagenfurt, Klagenfurt, Austria

    Gerhard Friedrich

  3. University of Klagenfurt, Klagenfurt, Austria

    Martin Gebser

  4. University of Klagenfurt, Klagenfurt, Austria

    Michael Morak

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Haldimann, J., Beierle, C., Kern-Isberner, G. (2021). Syntax Splitting for Iterated Contractions, Ignorations, and Revisions on Ranking Functions Using Selection Strategies. In: Faber, W., Friedrich, G., Gebser, M., Morak, M. (eds) Logics in Artificial Intelligence. JELIA 2021. Lecture Notes in Computer Science(), vol 12678. Springer, Cham. https://doi.org/10.1007/978-3-030-75775-5_7

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  • DOI: https://doi.org/10.1007/978-3-030-75775-5_7

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