The Decidability and Complexity of Order-Sorted Logic Programming for Ontologies and Rules with Argument Restructuring

Decidable reasoning between ontologies and rules is required for the Semantic Web. This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe order-sorted logic programming with sort, predicate, and metapredicate hierarchies for deriving predicate and meta-predicate assertions. Meta-level predicates (predicates of predicates) are useful for representing relationships between predicate formulas, and further, they conceptually yield a hierarchy similar to the hierarchies of sorts and predicates. By extending the order-sorted Horn-clause calculus, we develop a query-answering system that can answer queries such as atoms and meta-atoms generalized by containing predicate variables. We show that the expressive query-answering system computes every generalized query in single exponential time, i.e., the complexity of our query system is equal to that of DATALOG.