Action Emulation between Canonical Models

Abstract

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in [4].

Program models and semi-public environments

“…Following work by van Eijck et. al ( [31,19]) we propose a notion of 'equivalence' for program models. Our presentation is similar to the exposition of [27, Chapter 6, Section 6.1], here, we built on results presented there, and will focus in our proofs on the differences.…”

Learning Actions Models: Qualitative Approach

“…We say that two action models A 1 and A 2 are equivalent, written A 1 ≡ A 2 , if for any epistemic model M, M ⊗ A 1 ↔ M ⊗ A 2 , where ↔ denotes standard bisimulation on epistemic models [17].…”

Dynamic Epistemic Logics

“…In [24] a notion of parametrized action emulation is defined that characterizes action model equivalence. In [62,63] this is replaced by a nonparametrized action emulation relation, and it is shown that this characterizes action model equivalence for canonical action models (action models with maximal consistent subsets of an appropriate closure language as preconditions). The question whether non-parametrized action emulation also characterizes action model equivalence for arbitrary action models is still open.…”