Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses
arXiv:1811.07644 · doi:10.1007/978-3-030-17184-1_28
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.