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On Revocable and Irrevocable Belief Revision

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Krister Segerberg on Logic of Actions

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 1))

Abstract

Krister Segerberg proposed irrevocable belief revision, to be contrasted with ‘standard’ belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. In standard belief revision one can unmake (‘revoke’) belief in any formula, given yet further information that contradicts it. But irrevocable formulas remain believed forever. We compare traditional AGM belief revision with Segerberg’s dynamic doxastic logic, and with dynamic epistemic logical approaches to belief revision. Our work falls in the latter category. In that context with explicit belief operators and dynamic modal operators \([* \varphi ]\) for belief revision with \(\varphi \), we define revocable belief revision as belief revision satisfying that \(\psi \leftrightarrow [* \varphi ] [* \lnot \varphi ] \psi \) is valid; such that irrevocable means not revocable. Segerberg’s irrevocable belief revision is indeed irrevocable in that sense. We give semantic constraints (on multi-agent Kripke models) for revocable belief revision. In order for belief revision to be revocable: (i) the agents should consider the same states possible before and after revision, (ii) states that are non-bisimilar before revision may not be bisimilar after revision (if states are non-bisimilar, they can be distinguished from one another in the logical language), and (iii) it should be possible that states that are not equally plausible before revision become equally plausible after revision. We reformulate four well-known belief revision operators (hard update, soft update, conservative revision, severe revision) as qualitative dynamic belief revision operators. They are irrevocable in the (strong) sense above, because they violate one or more of these three requirements. However, single-agent severe revision is revocable in a weaker sense that following a revision \(*\varphi \) there is a sequence of further revisions recovering the initial state of belief. The work may be relevant for restricted-memory or other bounded rationality approaches to belief revision, e.g., when only a finite number of plausibility distinctions may be stored in memory. Therefore, it may be relevant for the study of logic and cognition.

I had the pleasure to be introduced by Greg Restall to Krister Segerberg at the Logic, Methodology and Philosophy of Science conference in 2003 in Oviedo, Spain. This was not entirely coincidental. I presented at that LMPS my first steps in modelling belief revision in dynamic epistemic logic, joint work with my Otago colleague Willem Labuschagne, rather an abstract than a formal publication: [47]. But from that initial study I had become acquainted with Segerberg’s work, and I was therefore eager to meet him. Our relationship has developed since. With great pleasure I recall the event organized at the University of Amsterdam by Olivier Roy where we met again in 2006. This was the 4th Paris-Amsterdam Logic Meeting of Young Researchers (PALMYR-4): Logics for Belief Dynamics. In 2008 we both became editors of the Journal of Philosophical Logic. In 2012 I still am, this a position I cherish, and I tend to feel that I owe it to Krister. The hospitality offered by Krister and Anita Segerberg, whereever they reside, is legendary. It need hardly be mentioned. But one should, on occasion.

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Notes

  1. 1.

    A prewellorder is a total, transitive and well-founded binary relation. A prewellorder induces an equivalence relation and a wellorder of equivalence classes.

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  1. University of Seville, Seville, Spain

    Hans van Ditmarsch

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Correspondence to Hans van Ditmarsch .

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  1. The John Paul II Catholic University of, Lublin, Poland

    Robert Trypuz

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Ditmarsch, H.v. (2014). On Revocable and Irrevocable Belief Revision. In: Trypuz, R. (eds) Krister Segerberg on Logic of Actions. Outstanding Contributions to Logic, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7046-1_10

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