A proof theoretical approach to default reasoning I: Tableaux for default logic

We present a general proof theoretical methodology for default systems. Given a default theory 〈W, D〉, the default rules D are simply understood as restrictions on the tableaux construction of the logic. Different default approaches have their own way of understanding these restrictions and executing them. For each default approach (such as Reiter, Brewka or Lukaszewicz), the allowable default extensions can be obtained from the default tableau construction. The advantage of our approach, besides being simple and neat, is in its generality: it allows for the development of a default theory for any logic with a tableau formulation, such as intuitionistic logic, linear logic or modal logic.