Iterated Belief Base Revision: A Dynamic Epistemic Logic Approach

Abstract

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 a 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.

Bringing Belief Base Change into Dynamic Epistemic Logic

“…As such, we can study operations of belief change based on preference models as transformations on grounded priority graphs. As a result, we obtain the representation of two postulates shown by Souza et al [30] to not be representable in such a manner. We also obtain a characterisation of relevant priority graph transformations, i.e., transformations that may be used to represent belief change operators, a problem that was left open in previous works, such as [23,31,30].…”

“…Definition 12 [30] Let ⋆ be a dynamic operator and † be a P-graph transformation. We say ⋆ is induced by † if for any preference model M and any P-graph G, if M is induced by G then the preference model ⋆(M, ϕ) is induced by the P-graph †(G, ϕ), where ϕ is any propositional formula in L 0 (P ), Some difficulties may arise in this connection since the relationship between P-graphs and preference models is not univocal, as exemplified by Fact 8.…”

“…For example, a graph transformation that changes the graph p ≺ q into the graph p ≺ q and the graph p ∧ q ≺ p ∧ ¬q ≺ ¬p ∧ q ≺ ¬p ∧ ¬q into p ∧ q ≺ ¬p ∧ q ≺ p ∧ ¬q ≺ ¬p ∧ ¬q cannot induce any dynamic operator since the original graphs are equivalent, i.e., induce the same models, but the resulting graphs are not. As such, Souza et al [30] define the notion of relevant graph transformation.…”

“…Definition 13 [30] We say that a P-graph transformation † is relevant if there is some dynamic operator ⋆ that is induced by it.…”

“…To characterise belief change postulates using graph transformations, Souza et al [30] provide a set of constraints on transformations that guarantee satisfaction to some postulates.…”