Belief revision within fragments of propositional logic

• We propose to adapt known revision operators for fragments of propositional logic.
• We provide natural criteria such adapted operators should satisfy.
• We use a general framework including all fragments captured via closure properties.
• We study the properties or our operators in terms of postulates.
• We give a preliminary complexity analysis of selected refined operators.

Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. Here we present a general approach to define new revision operators derived from known operators, such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual Horn, Krom and affine formulas, as well.