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We establish proof-theoretic, constructive and coalgebraic foundations forproof search in coinductive Horn clause theories. Operational semantics ofcoinductive Horn clause resolution is cast in terms of coinductive uniformproofs; its constructive content is exposed via soundness relative to anintuitionistic first-order logic with recursion controlled by the latermodality; and soundness of both proof systems is proven relative to a novelcoalgebraic description of complete Herbrand models.

Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses