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We give goal-oriented algorithms for discovering credential chains in RT_o, a role-based trust-management language introduced in this paper. The algorithms search credential graphs, a representation of RT_o credentials. We prove that evaluation based on reachability in credential graphs is sound and complete with respect to the set-theoretic semantics of RT_o . RT_o is more expressive than SDSI 2.0, so our algorithms can perform chain discovery in SDSI 2.0, for which existing algorithms in the literature either are not goal-oriented or require using specialized logic-programming inferencing engines. Being goal-oriented enables our algorithms to be used when credential storage is distributed. We introduce a type system for credential storage that guarantees well-typed, distributed credential chains can be discovered.