Abstract A consequence of a logic program is a consistent set of literals that are satisfied by every answer set. The well-founded model is a consequence that can be used to simplify the logic program. In this paper, we extend the notion of well-founded models to consequences for simplifying disjunctive logic programs (DLPs) in a general manner. Specifically, we provide two main notions, strong reliable set and weak reliable set, and show that a DLP is strongly equivalent to the simplified program if and only if the consequence is a strong reliable set, and they have the same answer sets if and only if the consequence is a weak reliable set. Then we provide computational complexity on identifying both notions. In addition, we provide an algorithm to compute some strong reliable sets and show that the approach is an extension of the well-founded model in simplifying logic programs.