Characterization of AGM Belief Contraction in Terms of Conditionals

Belief contraction is the operation of removing from the set K of initial beliefs a particular belief φ . One reason for doing so is, for example, the discovery that some previously trusted evidence supporting φ was faulty. For instance, a prosecutor might form the belief that the defendant is guilty on the basis of his confession; if the prosecutor later discovers that the confession was extorted, she might abandon the belief of guilt, that is, become open minded about whether the defendant is guilty or not. In their seminal contribution to belief change, Alchourrón, Gärdenfors and Makinson ([1]) defined the notion of "rational and minimal" contraction by means of a set of eight properties, known as the AGM axioms or postulates. They did so within a syntactic approach where the initial belief set K is a consistent and deductively closed set of propositional formulas and the result of removing φ from K is a new set of propositional formulas, denoted by K φ . We provide a new characterization of AGM belief contraction based on a so-far-unnoticed connection between the notion of belief contraction and the Stalnaker-Lewis theory of conditionals ([34, 21]).