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On Subtler Belief Revision Policies

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Logic, Rationality, and Interaction (LORI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10455))

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Abstract

This paper proposes three subtle revision policies that are not propositionally successful (after a single application the agent might not believe the given propositional formula), but nevertheless are not propositionally idempotent (further applications might affect the agent’s epistemic state). It also compares them with two well-known revision policies, arguing that the subtle ones might provide a more faithful representation of humans’ real-life revision processes.

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Notes

  1. 1.

    Still, there are proposals rejecting the postulate. In Sect. 3 the reader can find some of them and their relationship with this manuscript’s contents.

  2. 2.

    In [14] the plausibility relation is also conversely well-founded, forbidding infinite strictly ascending \(\le \)-chains. Here the domain is finite, so this requirement is satisfied automatically.

  3. 3.

    Formally, \(\mathopen {\varvec{\langle \!\!\!\,\,\langle }}\pi \mathclose {\varvec{\rangle \!\!\!\,\,\rangle }}^{M}_{w} := \mathopen {\{} {u \in W \mid (w,u) \in \mathopen {\varvec{\langle \!\!\!\,\,\langle }}\pi \mathclose {\varvec{\rangle \!\!\!\,\,\rangle }}^{M}} \mathclose {\}}\).

  4. 4.

    With \({\text {Mx}}^{k}(W) := \bigcup _{i=0}^{k} {\text {L}}_{i}(W)\). This is the plausibility-order-is-total version of the standard definition.

  5. 5.

    In particular, it can characterise all layers of any .

  6. 6.

    For success, Moorean phenomena [29] might appear. For idempotence, the \(\mathcal {L}\)-formula \(\mathop {[{\scriptstyle \varvec{>}}]} \bot \) characterises the bottommost elements of the ordering; thus, if the initial ordering is not flat (not all worlds equally plausible), each \(\mathop {[{\scriptstyle \varvec{>}}]} \bot \)-revision will move to the top different worlds.

  7. 7.

    Thus, is such that .

  8. 8.

    This relies on the fact that \(\chi \) is propositional: the set of \(\chi \)-worlds does not change.

  9. 9.

    If \({\text {lay}}^{\chi }_{\curlyvee } - {\text {lay}}^{\lnot \chi }_{\curlywedge } < 0\), then there is already a strong belief on \(\chi \) at M, and any \(m \ge 0\) works.

  10. 10.

    Thus, is such that .

  11. 11.

    Thus, is such that .

  12. 12.

    If \({\text {lay}}^{\chi }_{\curlywedge } - {\text {lay}}^{\lnot \chi }_{\curlywedge } < 0\), then there is already a belief on \(\chi \) at M, and any \(m \ge 0\) works.

  13. 13.

    Some forms of propaganda are based on this.

  14. 14.

    Still, the axiom system for the general layered upgrade already provides a syntactic (albeit indirect) characterisation of the presented policies.

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Authors and Affiliations

  1. Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Fernando R. Velázquez-Quesada

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  1. Fernando R. Velázquez-Quesada
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Correspondence to Fernando R. Velázquez-Quesada .

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Editors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam , Amsterdam, Noord-Holland, The Netherlands

    Alexandru Baltag

  2. Department of Philosophy, The University of Auckland, Auckland, Auckland, New Zealand

    Jeremy Seligman

  3. Graduate School of Letters, Hokkaido University , Sapporo, Japan

    Tomoyuki Yamada

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Velázquez-Quesada, F.R. (2017). On Subtler Belief Revision Policies. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_22

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