What if no hybrid reasoner is available? Hybrid MKNF in multi-context systems

Abstract

In open environments, agents need to reason with knowledge from various sources, represented in different languages. Multi-Context Systems (MCSs) allow for the integration of knowledge from different heterogeneous sources in an effective and modular way. Whereas most knowledge bases (contexts) typically considered within an MCS are written in some description logic or some non-monotonic rule-based language, sometimes more expressive languages that combine the features of both these paradigms are necessary, such as Hybrid MKNF. However, since agents may not have access to specialized reasoners for contexts using all these languages, it proves useful to have tools that equivalently simplify or transform a given MCS into another MCS that only uses the reasoners that are available. In this article, we thoroughly investigate the relation between MCSs and Hybrid MKNF. We provide a number of transformations that show that Hybrid MKNF knowledge bases can be embedded into MCSs without the need for specific MKNF reasoners. To complete the picture, we also show that when an MKNF reasoner is available, it can be used to handle several description logic and rule contexts joined into a single MKNF context. Furthermore, we show that we can encapsulate the non-monotonic transfer of information between different contexts in one rule language context, allowing e.g. the use of external non-monotonic reasoners.