On the Logic of Small Changes in Theories II

Abstract

The idea that it might be worth investigating the logic of theory change, in the sense of the present paper, is due, independently to Carlos Alchourrón and David Makinson on the one hand and to Peter Gärdenfors on the other. Their joint paper [1] is the most substantial contribution to this area to date. The idea is that if T is a theory (which we think of as a set of formulae) and A is a formula, then T + A is a new theory, the theory which results if A is “added” to T. What makes this notion problematic — and interesting — is that this operation is supposed to be defined even when A is inconsistent with T.