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Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses (1811.07644v3)
Published 19 Nov 2018 in cs.LO
Abstract: We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its constructive content is exposed via soundness relative to an intuitionistic first-order logic with recursion controlled by the later modality; and soundness of both proof systems is proven relative to a novel coalgebraic description of complete Herbrand models.