Description logics with aggregates and concrete domains

摘要

Description logics are a family of knowledge representation formalisms well suited for intentional reasoning about conceptual models of databases/data warehouses. We extend description logics with concrete domains (such as integers and rational numbers) that include aggregation functions over these domains (such as min, max, count, and sum) which are usually available in database systems. We show that the presence of aggregation functions may easily lead to undecidability of (intentional) inference problems such as satisfiability and subsumption. However, there are also extensions for which satisfiability and subsumption are decidable, and we present decision procedures for the relevant inference problems.