Belief revision is a fundamental ability for an autonomous agent, that should be able to correct her beliefs when evidence contradicts them. In this talk we will recall the framework of iterated belief revision, following Darwiche and Pearl's approach and its developments. In particular this approach works on abstract objects called epistemic states. We will discuss what can be some interesting candidates for representing these abstract objects, through the definition of epistemic spaces. And we will see if TPO (total-pre-orders on interpretations) or OCF (Ordinal Conditional Functions) are acceptable candidates to be considered as potential canonical representations of these epistemic states.
on TPO is interesting and can prove to be useful for many
applications, it is not the whole class of Darwiche and
Pearl’s iterated revision operators. Some works [
Then an interesting question is to investigate the pos- This work has benefited from the support of the AI sible candidates for the representation of these iterated Chair BE4musIA of the French National Research Agency revision operators, and to look for some canonical rep- (ANR-20-CHIA-0028). resentation. It is possible to define a function of instantiation between two representations (that will be called References epistemic spaces). These functions can be interesting to show for instance that an epistemic space is more general than another one. And then the question of the canonical representation is to find a top element for this relation.
In fact, Darwiche and Pearl’s epistemic states being abstract objects, the whole class is very general, and one can show that no countable representation can be adequate. But if we add another sensible property we can reach such a result of a canonical representation. First, note that, whatever the chosen representation, every epistemic state can be viewed as a black box associating each finite sequence of formulae with a formula representing the beliefs of the agent after the successive revision of the epistemic state by each formula from the sequence. Based on that observation, two epistemic states are strongly equivalent according to a revision operator if they cannot be distinguished from each other by any such successive revision steps, which means that these epistemic states have the same behavior for that revision operator. Now the (very natural) assumption is that every epistemic state is reachable from an initial, “empty”, epistemic state, through a finite succession of revisions.
If we make this assumption, then OCFs are a possible candidate of canonical representation of epistemic states.
OCFs were proposed long ago by Spohn [
But if one supposes that we start from an initial “empty”
epistemic state, then several operators can be define that
produce OCFs without the need of extra numerical
information [
Acknowledgments Representation of Darwiche and Pearl’s Epistemic States for Iterated Belief Revision, in: Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning (KR’22), 2022, pp. 320–330.