Belief Contraction Within Fragments of Propositional Logic

Recently, belief change within the framework of fragments of propositional logic has gained attention. In the context of revision it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. In this paper we generalize this notion of refinement to belief change operators. Whereas the notion of refinement allowed one to define concrete rational operators adapted to propositional fragments in the context of revision and update, it has to be specified for contraction. We propose a specific notion of refinement for contraction operators, called reasonable refinement. This allows us to provide refined contraction operators that satisfy the basic postulates for contraction. We study the logical properties of reasonable refinements of two well-known model-based contraction operators. Our approach is not limited to the Horn fragment but applicable to many fragments of propositional logic, like Horn, Krom and affine fragments.