Deviation in Belief Change on Fragments of Propositional Logic

It is known that prominent fragments of propositional logic are not closed under standard belief change operators. That is, applying such operators to knowledge bases in a fragment may produce results that have no equivalent in the same language. However, the potential range of such a deviation has not been investigated yet. In this paper, we give a systematic study of this problem by considering four prominent change operators (Dalal, Satoh, Winslett, and Forbus) and three important fragments (1CNF, Krom, and Horn). While all operators are shown to be closed under the 1CNF fragment, we observe that for the other two fragments the behavior of the operators significantly differs. We expect our considerations on deviation to play an important role in the design of change operators for concrete Knowledge Representation formalisms.