Beliefs, belief revision, and splitting languages
Rohit Parikh · Center for the Study of Language and Information eBooks · 1999
Much current work in the study of belief revision goes back to a now classic paper due to Alchourron, Gardenfors and Makinson [AGM]. The central issue is how to revise an existing set of beliefs T to a new set of beliefs T ∗A when a new piece of information A is received. If A is consistent with T , then it is easy: we just add A to T and close under logical inference to get the new set of beliefs. The harder problem is how to revise the theory T when a piece of information A inconsistent with T is received. Clearly, as Levi has suggested, T must first be contracted to a smaller theory T ′ = T • − ¬A which is consistent with A and then A added to T ′. However, it is not clear how T • − ¬A should be obtained. The mere deletion of ¬A from T will clearly not leave us with a theory and there is in general no unique way to get a theory T ′ which is contained in T and does not contain ¬A.