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This paper presents a determinacy inference analysis for logic programs. The analysis infers determinacy conditions that, if satisfied by a call, ensures that it computes at most one answer and that answer is generated only once. The principal component of the technique is a goal-independent analysis of individual clauses. This derives a condition for a call that ensures only one clause in the matching predicate possesses a successful derivation. Another key component of the analysis is backwards reasoning stage that strengthens these conditions to derive properties on a call that assure determinacy. The analysis has applications in program development, implementation and specialisation.