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.
CITATION STYLE
Basold, H., Komendantskaya, E., & Li, Y. (2019). Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11423 LNCS, pp. 783–813). Springer Verlag. https://doi.org/10.1007/978-3-030-17184-1_28
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