Learning-theoretic take on:
Belief Revision on Plausibility States
“Irrevocable knowledge” given by partition models is generally criticized in epistemology as representing a unrealistic concept, not fit to represent the knowledge we possess in day-to-day life or in natural sciences. […] We relax our notion of knowledge in order to be generous to the learning agent, not requiring him to achieve an unrealistic standard of certainty: it is enough if his beliefs reliably (and justifiably) converge to full truth.
Baltag, Gierasimczuk & Smets, “Belief Revision as a Truth-tracking Process”
In the final lecture we will go through the framework of analyzing the truth-tracking properties of belief revision policies defined on plausibility states. On the side of belief revision we will follow the lines of the semantics of dynamic epistemic logic: beliefs of the agent is the content of those possible worlds that he considers most plausible; the revision results both in the change of the current belief, but can also induce modification of the plausibility order. In this context we will be concerned with the limiting properties of belief-revision understood as learning: identifying the actual world among the initial domain of the epistemic state. We will see that the ability to reliably learn is related to the ability to separate hypotheses by observations; hence, learnability can be viewed as a topological separation property.
The results will concern mostly the conditions for universality of a belief revision policy (i.e., for a belief revision method being as powerful as full identification in the limit). This will lead to identifying factors that influence the (non-)universality of a belief-revision policy: the prior conditions for belief revision (e.g., well-founded plausibility states); type of incoming information (e.g., entirely truthful as opposed to partially erroneous); properties of belief-revision-based learning functions (e.g., conservatism).
Baltag, A., Gierasimczuk, N., and Smets, S. (2011). Belief Revision as a Truth-Tracking Process, in: Krzysztof R. Apt (Ed.): Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-2011), ACM 2011.
Gierasimczuk, N. (2010). Knowing One’s Limits. Logical Analysis of Inductive Inference (Chapter 4), PhD Thesis, University of Amsterdam.