Towards General Representability in Knowledge Exchange

In data exchange, one is typically given a source database instance and a mapping between a source schema and a target schema. The goal then is to materialize a target database instance that corresponds to the source instance and the mapping. In this setting source data is explicitly given, that is, every fact that is true in it is explicitly mentioned in the source database instance. Knowledge bases typically consist of some explicit knowledge – like in database instances – and some implicit knowledge, usually given in the form of rules that specify how to derive knowledge not explicitly stored. In [5], Arenas et al. introduced the setting of knowledge exchange, where one is given a source knowledge base and a mapping between a source schema and a target schema, and the goal is to materialize a target knowledge base, that is, both explicit and implicit knowledge. While the question of what constitutes a “good” solution to a data exchange problem has been the topic of research in recent years [11], the question of what constitutes a “good” solution to a knowledge exchange problem is rather new. In particular, there are now two components, explicit and implicit knowledge, which play rather different roles in what we expect from them. In [5], two especially desirable properties of the target knowledge base were identified. First, one generally wants to minimize explicit knowledge, thus generating as much knowledge by rules as possible. Second, in typical knowledge-based systems (such as those based on RDFS, OWL, or general description logics), the explicit knowledge changes frequently, but the implicit knowledge remains constant over a longer time. Hence, it is desirable to let the target implicit knowledge only depend on the implicit knowledge at the source and the mapping between source and target. Thus, knowledge exchange effectively becomes a two-stage process: