Nonmonotonic reasoning and modal logic, from negation as failure to default logic

We present a modal characterization of two well-known nonmonotonic formalisms : the negation as failure rule and default logic. The semantics of logic programming with the negation as failure rule is described through the definition of a modal completion. In modal logic K4, this completion characterizes provability in logic programming with respect to SLDNF-resolution while in modal logic Pr (the modal logic of provability) it characterizes unprovability in logic programs.