Horn functions form a subclass of Boolean functions possessing interesting structural and computational properties. These functions play a fundamental role in algebra, artificial intelligence, combinatorics, computer science, database theory, and logic. In a recent paper titled Hypergraph Horn functions, we introduce the subclass of hypergraph Horn functions that generalizes matroids and equivalence relations. We provide multiple characterizations of hypergraph Horn functions in terms of implicate-duality and the closure operator, which are respectively regarded as generalizations of matroid duality and Mac Lane-Steinitz exchange property of matroid closure. We also study algorithmic issues on hypergraph Horn functions.