Ranking kinematics for revising by contextual information

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.

Revision by Conditionals: From Hook to Arrow

The belief revision literature has largely focussed on the issue of how to revise one’s beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How to model agents capable of acquiring information regarding which rules of inference (‘Ramsey Test conditionals’) they ought to use in reasoning about these facts. Our approach to this second question of so-called ‘conditional revision’ is distinctive insofar as it abstracts from the controversial details of how the address the first. We introduce a ‘plug and play’ method for uniquely extending any iterated belief revision operator to the conditional case. The flexibility of our approach is achieved by having the result of a conditional revision by a Ramsey Test conditional (‘arrow’) determined by that of a plain revision by its corresponding material conditional (‘hook’). It is shown to satisfy a number of new constraints that are of independent interest.

Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state.

Iterated Belief Base Revision: A Dynamic Epistemic Logic Approach

AGM’s belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent’s belief state - whether representing the agent’s ‘explicit beliefs’ or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. This work investigates how priority graphs, a syntactic representation of preference relations deeply connected to prioritised bases, can be used to characterise belief change operators, focusing on well-known postulates of Iterated Belief Change. We provide syntactic representations of belief change operators in a dynamic context, as well as new negative results regarding the possibility of representing an iterated belief revision operation using transformations on priority graphs.

Iterated Belief Revision

A discussion of the problem of extending the basic AGM belief revision theory to iterated belief revision: the problem of formulating rules, not only for revising a basic belief state in response to potential new evidence, but also for revising one’s revision rules in response to potential new evidence. The emphasis in the chapter is on foundational questions about the nature of and motivation for various constraints, and about the methodology of the evaluation of putative counterexamples to proposed constraints. Some specific constraints that have been proposed are criticized. The chapter emphasizes the importance of meta-information—information about one’s sources of information—and argues that little of substance can be said about constraints on iterated belief revision at a level of abstraction that lacks the resources for explicit representation of meta-information.

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

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.

Strong Syntax Splitting for Iterated Belief Revision

AGM theory is the most influential formal account of belief revision. Nevertheless, there are some issues with the original proposal. In particular, Parikh has pointed out that completely irrelevant information may be affected in AGM revision. To remedy this, he proposed an additional axiom (P) aiming to capture (ir)relevance by a notion of syntax splitting. In this paper we generalize syntax splitting from logical sentences to epistemic states, a step which is necessary to cover iterated revision. The generalization is based on the notion of marginalization of epistemic states. Furthermore, we study epistemic syntax splitting in the context of ordinal conditional functions. Our approach substantially generalizes the semantical treatment of (P) in terms of faithful preorders recently presented by Peppas and colleagues.