Day 5: Friday, August 16th 2013

Learning-theoretic take on:

Belief Revision via Contraction

The theory of belief revision invites us to view empirical inquiry as the process of revising one’s background theory by evidence that accumulates in the environment. We take the revision-based scientist to give formal substance to the idea.

Martin & Osherson, “Elements of Scientific Inquiry”

The lecture will cover the “inquiry via belief revision” proposal of Martin & Osherson (1998). We will discuss the class of “rational” scientists that keep on revising their beliefs in the light of incoming data, starting from some background theory. The inquiry is initiated from a set of formulas and the incoming datum is a formula of the same language. Hence, belief revision is a function of two arguments that yields a new belief. As in the well known AGM paradigm, the function will be defined to work in two steps: first, formulas that are incompatible with the new datum are removed from the belief set (belief contraction), then the new datum is added in (belief revision).

We will devote some attention to the process of contraction (maxichoice and stringent contraction) and (iterated) revision defined from it. Then we will focus on the central topic: linguistic scientists based on revision, i.e., learning functions that change their belief sets, and their hypotheses, by means of the previously defined belief revision policy, and we will discuss their inductive inference power. We will also analyze the importance of the background theory and how it can be augmented to facilitate inquiry. Time permitting, in the end we will discuss the possibility of efficient inquiry via such understood belief revision.

Bibliography:

  1. Martin, E., and Osherson, D. (1997). Scientific Discovery Based on Belief Revision, The Journal of Symbolic Logic, Vol. 62, No. 4, pp. 1352-1370.
  2. Martin, E., and Osherson, D. (1998). Elements of Scientific Inquiry, Cambridge: MIT Press.

Slides