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Conditional Descriptor Revision and Its Modelling by a CSP

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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

Descriptor revision is a belief change framework that was introduced by Hansson as an alternative to the currently prevailing AGM paradigm. One central idea of descriptor revision is to describe the desired outcome of a belief change. Thus, descriptor revision allows expressing different kinds of belief change operations like revision or contraction in a structured and combined way. In this paper, we investigate the framework of conditional descriptor revision. Conditional descriptor revision is a variation of descriptor revision aimed at the revision of ranking functions in the context of conditional logic. It is obtained by applying descriptor revision to conditional logic and additionally requiring the belief changes to fulfil the principle of conditional preservation. We show how conditional descriptor revision can be characterized by a constraint satisfaction problem (CSP). In contrast to previous work, we cover the full descriptor language over conditionals closed under conjunction, disjunction, and negation. We also line out an implementation of conditional descriptor revision based on its CSP representation. Since propositional logic can be embedded into conditional logic, our approach also provides descriptor revision for propositional logic.

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Notes

  1. 1.

    In the original framework by Hansson this is much more elaborated. Following the terminology of Hansson, here we present a form of local deterministic monoselective descriptor revision [18]. Moreover, we primarily focus on one change, while Hansson designs the framework for change operators.

  2. 2.

    All \( \kappa _0, \gamma _i^+, \gamma _i^- \) can be rational [22], but \( \kappa ^\circ \) has to satisfy the requirements for an OCF, in particular, all \( \kappa ^\circ (\omega ) \) must be non-negative integers. In this paper, it suffices to assume \( \kappa _0, \gamma _i^+, \gamma _i^- \) to be integers and we will thus focus on the case \(\vec {\gamma } \in \mathbb {Z}^{2n}\).

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Acknowledgements

We thank the anonymous reviewers for their valuable hints and comments that helped us to improve the paper. 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). Kai Sauerwald is supported by the grant BE 1700/9-1.

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Authors and Affiliations

  1. FernUniversität in Hagen, 58084, Hagen, Germany

    Jonas Haldimann, Kai Sauerwald, Martin von Berg & Christoph Beierle

  2. TU Dortmund University, 44227, Dortmund, Germany

    Gabriele Kern-Isberner

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  1. Jonas Haldimann
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  2. Kai Sauerwald
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  4. Gabriele Kern-Isberner
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  5. Christoph Beierle
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Correspondence to Jonas Haldimann .

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  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., Sauerwald, K., von Berg, M., Kern-Isberner, G., Beierle, C. (2021). Conditional Descriptor Revision and Its Modelling by a CSP. 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_4

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  • DOI: https://doi.org/10.1007/978-3-030-75775-5_4

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