Building Theories into Instantiation

Abstract

Instantiation orderings over formulas (the relation of one formula being an instance of another) have long been central to the study of automated deduction and logic programming, and are of rapidly-growing importance in the study of database systems and machine learning. A variety of instantiation orderings are now in use, many of which incorporate some kind of background information in the form of a constmint theory. Even a casual examination of these instantiation orderings reveals that they are somehow related, but in exactly what way? This paper presents a general instantiation ordering of which all these orderings are special cases, as are other instantiation orderings. The paper shows that this general ordering has the semantic properties we desire in an instantiation ordering, implying that the special cases have these properties as well. The extension to this general ordering is useful in applications to inductive logic programming, automated deduction and logic programming, knowledge-base vivification, and database systems.