Domain Reasoning In TopKAT: Reduction and Completeness
summary
TopKAT is incomplete over relational models: there exists an inequality true in every relational TopKAT but unprovable from TopKAT axioms, yet adding that inequality as an axiom restores completeness. The work proves TopKAT is complete for domain/codomain comparison completeness of KAT terms by a streamlined reduction to regular languages and a complete interpretation of traces; tools are universal-algebra reductions and language-model embeddings, and the encoding of under‑approximate specifications still works despite the global incompleteness.
AI-written summary · about