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.
Highlights
In multi-agent systems, it is crucial for agents working together to represent and to reason with beliefs coming from different contexts independently
In [21], Sezgin and Kern-Isberner presented a property for revising epistemic states by conditionals in the framework of ranking functions which they called Generalized Ranking Kinematics (GRK) that can be seen as an analog to Subset Independence for qualitative belief revision. (GRK) connects Jeffrey’s Rule to the axioms of inductive inference introduced by Shore and Johnson and can be seen as an extension of Spohn’s work on transferring Jeffrey’s rule to the framework of ranking functions
– We show that strategic c-revisions satisfy the Ramsey Test for conditional revision. – We show to reconstruct a full c-revised ranking function from the conditionalized crevised sub-ranking functions by making use of non-normalized OCFs and a simple merging operator. – We present a new revision operator for pre-OCFs which is based on strategic c-revision and called pre-c-revision, and investigate the relation between the revision on local contexts versus the global revision with the complete set of conditionals. – We investigate pre-c-revisions in the light of postulates for revisions with sets of conditionals, which we derive from the postulates for conditional revision from [13]
Summary
In multi-agent systems, it is crucial for agents working together to represent and to reason with beliefs coming from different contexts independently. (CondPS) Let ∗ be a revision operator that takes epistemic states Ψ and sets of conditionals Δ resp. The concept of Generalized Ranking Kinematics, which we introduced in [21] and will discuss in this paper would state that, first, the plausibility of cases (expressed by S) does not affect the conditional belief for each case Ai, and second, that for the posterior conditional belief given Ai only the respective new information Δi is relevant. In [21], Sezgin and Kern-Isberner presented a property for revising epistemic states by conditionals in the framework of ranking functions which they called Generalized Ranking Kinematics (GRK) that can be seen as an analog to Subset Independence for qualitative belief revision.
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