Belief Contraction and Erasure in Fragments of Propositional Logic

International audienceRecently, belief change within the framework of fragments of propositionallogic has gained attention. In the context of revision it has been proposed to refineexisting operators so that they operate within propositional fragments, and that theresult of revision remains in the fragment under consideration. Later this notionof refinement was generalized to belief change operators. Whereas refinement al-lowed one to define concrete rational operators adapted to propositional fragmentsin the context of revision and update, it has to be specified for contraction anderasure. We propose a specific notion of refinement for contraction and erasureoperators, called reasonable refinement. This allows us to provide refined contrac-tion and erasure operators that satisfy the basic postulates. We study the logicalproperties of reasonable refinement of two model-based contraction operators andtwo model-based erasure operators. Our approach is not limited to the Horn frag-ment but applicable to many fragments of propositional logic, like Krom and affinefragment