On the logic of theory change: safe contraction
This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of ''safe contraction'' of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and under various natural constraints. The leading idea is simple. Let A be a set of propositions, \(<\) a non- circular relation over A, and x a proposition that we wish to eliminate from A. The authors call an element a of A ''safe'' with respect to x (modulo \(<\), and given some background consequence operation Cn) iff it is not a minimal element (under \(<)\) of any minimal subset (under inclusion) B of A such that \(x\in Cn(B)\); and putting A/x to be the set of safe elements of A, they define the function of safe contraction by setting \(A\dot- x=A\cap Cn(A/x)\).
scientific article; zbMATH DE number 3976989