ON INFORMATION FUNCTIONS PART TWO: APPLICATIONS TO THE LOGIC OF THEORY CHANGE
Krzysztof Szymanek · 2006
The purpose of this work is to show how the notion of information function introduced in [1] can be used in the logic of theory change devel-oped by P. Gärdenfors, C. E. Alchourron and D. Makinson in [2], [3] and [4]. The simplest and best known form of theory change is expansion, where a new position, if consistent with a given theoryK, is set-theoretically added to K and this expanded set is then closed under logical consequence. Second form is theory contraction, where a proposition α, which was earlier in a theory K, is rejected. The basic problem is to determine which propo-sitions should be rejected along with α so that the contracted theory will be closed under logical consequence. Third kind of change is revision, where a proposition, in general inconsistent with a given theory K, is added to K under the requirement that the revised theory be consistent and closed under logical consequence. In this note we shall focus on the contraction functions, i.e. functions which reflect the process of contraction according to Gärdenfors postulates (see definition B.1.). We will point how using the notions presented in Part One can be proved a few important theorems about contraction functions (in the less general case than in [2] and [3], where C is not necessarily the classical consequence). Our leading idea is rather intuitive. Loosely speaking, a proposition α is rejected from a theory K if at least a part of information contained in α has lost its credibility and the contraction operation is to reject, along with α, those formulas which contain any component of “bad ” information.