Ranking kinematics for revising by contextual information

Abstract

Probability kinematics is a leading paradigm in probabilistic belief change. It is based on the idea that conditional beliefs should be independent from changes of their antecedents’ probabilities. In this paper, we propose a re-interpretation of this paradigm for Spohn’s ranking functions which we call Generalized Ranking Kinematics as a new principle for iterated belief revision of ranking functions by sets of conditional beliefs with respect to their specific subcontext. By taking into account semantical independencies, we can reduce the complexity of the revision task to local contexts. We show that global belief revision can be set up from revisions on the local contexts via a merging operator. Furthermore, we formalize a variant of the Ramsey-Test based on the idea of local contexts which connects conditional and propositional revision in a straightforward way. We extend the belief change methodology of c-revisions to strategic c-revisions which will serve as a proof of concept.

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Open Access funding enabled and organized by Projekt DEAL.

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Correspondence to Meliha Sezgin.

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Sezgin, M., Kern-Isberner, G. & Beierle, C. Ranking kinematics for revising by contextual information. Ann Math Artif Intell (2021). https://doi.org/10.1007/s10472-021-09746-2

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Keywords

  • Iterated belief revision
  • Kinematics
  • Spohn’s ranking functions
  • Jeffrey’s rule

Mathematics Subject Classification (2010)

  • 68T30 Knowledge representation