Infobase Change: A First Approximation

Abstract

Generalisations of theory change involving operations on arbitrary sets of wffs instead of on belief sets (i.e., sets closed under a consequence relation), have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, which means that it can be employed to determine the theory contraction operation associated with a base contraction operation. In this paper we follow such an approach as the first step in defining infobase change. We think of an infobase as a finite set of wffs consisting of independently obtained bits of information. Taking AGM theory change (Alchourron et al. 1985) as the general framework, we present a method that uses the structure of an infobase B to obtain an AGM theory contraction operation for contracting the belief set Cn(B). Both the infobase and the obtained theory contraction operation then play a role in constructing a unique infobase contraction operation. Infobase revision is defined in terms of an analogue of the Levi Identity, and it is shown that the associated theory revision operation satisfies the AGM postulates for revision. Because every infobase is associated with a unique infobase contraction and revision operation, the method also allows for iterated base change.