Centralized Reasoning Translation and Its Computing Complexity for Heterogeneous Semantic Mappings

Abstract

Bridge rules provide an important mechanism for describing semantic mapping and propagating knowledge for distributed dynamic description logics (D3L). The current research focuses on the homogeneous bridge rules that only contain atomic elements. In this paper, the research is extended to the D3L reasoning problem with heterogeneous bridge rules that contain composite elements in subset ends. The regularity of the distributed knowledge base is defined. Through the alteration of the bridge rules and transforming different forms into existing language mechanisms, we present an algorithm that can convert the D3L knowledge base with dynamic description logic ${\mathcal{DSROIQ}}$ as the local ontology language into a single ${\mathcal{DSROIQ}}$ knowledge base. Next, we study the properties of the algorithm. We prove that the algorithm will terminate in polynomial time and that the satisfiability of the target knowledge base is equivalent to the satisfiability of the original knowledge base. Thus, we prove that the worst-case time complexity of the centralized reasoning on the regular D3L knowledge base with such bridge rules is the same as that on a single ${\mathcal{DSROIQ}}$ knowledge base. The method proposed in this paper makes centralized reasoning for D3L obtain the same worst-case time complexity as the existing distributed reasoning method and solves the problem that the latter cannot handle heterogeneous composite bridge rules.