Nonmonotonic reasoning has been explored as a form of abductive reasoning
where default assumptions are treated as abductive hypotheses. While the
semantics and proof theories under this approach have been studied
extensively, the question of how disjunctive programs may be used to reason
abductively has rarely been investigated. At the center of the question is
how to embed disjunctive reasoning into that of negation-as-failure. A more
concrete question is about whether the elegant abductive proof procedure by
Eshghi and Kowalski can be extended to answer queries for disjunctive
programs, and if yes, what is the semantics that such an extended procedure
computes. In this paper we answer these questions by formulating a
semantics, the regular extension semantics, for disjunctive programs, and
by presenting a sound and complete extension of the Eshghi-Kowalski
procedure, called disjunctive EK procedure, for query answering with
respect to ground disjunctive programs under this semantics.