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This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from other information in a program. These semantics are based on lattice-structured multi-valued logics, and are characterized by a new fixpoint semantics of extended disjunctive programs. Applications of the paraconsistent semantics for reasoning in inconsistent programs are also presented.