Day 3: Wednesday, August 14th 2013

Learning-theoretic take on:

Belief Revision and Possible Histories

A conservative methodologist seeks to minimize the damage done to his current beliefs by new information. A reliabilist, on the other hand, seeks to find the truth whatever the truth might be. […] The inductive leap from a hundred black ravens to the universal generalization that all ravens are black is not conservative. Nor was Copernicus’ revolutionary rejection of conservative tinkering within the Ptolemaic system. […] Conservatism is the motivation behind the theory of belief revision proposed by [AGM]. Reliabilism is the principal concern of formal learning theory.

Kelly, Schulte & Hendricks, “Reliable Belief Revision”

This lecture will cover the “reliability of belief revision” analysis of Kelly (1998). The results rest on Spohn’s approach to belief revision: an agent’s epistemic state is given by an assignment of degrees of implausibility to possible worlds; the actual belief is taken to be the proposition satisfied by the possible worlds of implausibility degree zero. We will discuss various revision operators that differ in how they change the implausibility order on possible worlds.

The inductive inquiry frameworks adopted here is that of prediction: the successive propositions received by the agent are true reports of successive outcomes of some discrete, sequential experiment. The goal of learning is to arrive at a sufficiently informative belief state that allows predicting how the sequence might possibly evolve in the unbounded future. The agent’s task is to stabilize on such a hypothesis for each outcome sequence admitted by the inductive problem. Within this framework of inductive inquiry we will analyze the learning power (reliability) of concrete belief revision methods of Spohn (1988), Boutilier (1993), Nayak (1994), Goldszmidt and Pearl (1994), and Darwiche and Pearl (1997). Time permitting, we will discuss the concept of inductive amnesia:  the property of belief revision operators that signifies the trade-off between remembering the past data and the ability of predicting the future results of the experiment.

grue_round

Bibliography:

  1. Kelly, K. (1998). Iterated Belief Revision, Reliability, and Inductive Amnesia, Erkenntnis, Vol. 50, pp. 11-58.
  2. Kelly, K. (1998). The Learning Power of Iterated Belief Revision, in: Proceedings of the Seventh TARK Conference, Itzhak Gilboa (ed.), pp. 111-125.
  3. Kelly, K., Schulte, O., and Hendricks, V. (1997). Reliable Belief Revision, in: Logic and Scientfic Methods, M. L. Dalla Chiara, et al. (eds.), Dordrecht: Kluwer.

Slides