  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 the present paper, 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, and show that the
recognition problem (i.e., deciding if a given definite Horn CNF represents a
hypergraph Horn function) and key realization (i.e., deciding if a given
hypergraph is realized as a key set by a hypergraph Horn function) can be done
in polynomial time, while implicate sets can be generated with polynomial
delay.
