What kind of independence do we need for multiple iterated belief change?

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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“…for all ω ∈ Ω via the merging operator M(•). Thus, (22) follows from (18) via normalization for all ω ∈ Ω.…”

Section: Pre-c-revisionsmentioning

confidence: 99%

Ranking kinematics for revising by contextual information

Sezgin

Kern-Isberner

Beierle

2021

Ann Math Artif Intell

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“…We now show that every c-contraction, that is defined by (13) and fulfills Proposition 3, is of the form (14) or (15). Let κ A = κ be such a c-contraction that fulfills (1), i.e.…”

Section: Iterated Contraction By a Single Propositionmentioning

confidence: 81%

“…Obviously, the postulates for conditional revision as elaborated by Kern-Isberner [14] are also fulfilled by revisions in this special case; a detailed elaboration of the properties of revisions under the principle of conditional preservation by a single conditional can be found in [12,15].…”

Section: Iterated Belief Change Under the Principle Of Conditional Prmentioning

confidence: 85%

“…which corresponds to equation (15). case 2: In the second case we have κ(A) > 0, which implies κ(A) = 0, κ = min( A , κ ).…”

Section: Iterated Contraction By a Single Propositionmentioning

confidence: 97%

“…We will now prove that fulfills (IC3) -(IC4) under the given presuppositions. According to Theorem 6 and 8, every contraction that satisfies (PCP ocf ) and (AGMes-1) -(AGMes-7) has either the form (14) or the form (15). Let ω 1 ∈ A , ω 2 ∈ A and κ = κ A.…”

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 99%

See 2 more Smart Citations

Iterated contraction of propositions and conditionals under the principle of conditional preservation

Kern-Isberner¹,

Bock²,

Sauerwald³

et al.

EPiC Series in Computing

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Research on iterated belief change has focussed mostly on belief revision, only few papers have addressed iterated belief contraction. Most prominently, Darwiche and Pearl published seminal work on iterated belief revision the leading paradigm of which is the so-called principle of conditional preservation. In this paper, we use this principle in a thoroughly axiomatized form to develop iterated belief contraction operators for Spohn's ranking functions. We show that it allows for setting up constructive approaches to tackling the problem of how to contract a ranking function by a proposition or a conditional, respectively, and that semantic principles can also be derived from it for the purely qualitative case.

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