First-Order Default Logic Revisited

Reiter's original proposal for default logic is unsatisfactory for open default theories because of Skolemization and grounding. In this paper, we reconsider this long-standing problem and propose a new world view semantics for first-order default logic. Roughly speaking, a world view of a first-order default theory is a maximal collection of structures satisfying the default theory where the default part is fixed by the world view itself. We show how this semantics generalizes classical first-order logic and first-order answer set programming, and we discuss its connections to Reiter's semantics and other related semantics. We also argue that first-order default logic under the world view semantics provides a rich framework for integrating classical logic based and rule based formalisms in the first-order case.