Computational and structural aspects of openly specified type hierarchies

Abstract. One may identify two main approaches to the description of type hierarchies. In total specification, a unique hierarchy is described. In open specification, a set of constraints identifies properties of the hierarchy, without providing a complete description. Open specification provides increased expressive power, but at the expense of considerable computational complexity, with essential tasks being NP-complete or NP-hard. In this work, a formal study of the structural and computational aspects of open specification is conducted, so that a better understanding of how techniques may be developed to address these complexities. In addition, a technique is presented, based upon Horn clauses, which allows one to obtain answers to certain types of queries on open specifications very efficiently. 1