Modal Logic Applied to Query Answering and the Case for Variable Modalities

We present a query answering technique based on notions and results from modal Correspondence Theory. It allows us to answer a wide family of conjunctive queries by polynomial reduction to knowledge base satisfiability problem. An advantage of this technique lies in its uniformity: it does not depend on a Description Logic (DL), so that extending a DL does not invalidate the algorithm. Thus, the problem of answering queries in this family is decidable in any decidable DL. The construction also leads to an idea of extending the modal language with so called variable modalities, whose syntax and semantics is introduced in the paper. On the one hand, this yields a broader family of queries that can be answered with the same technique. On the other hand, modal logic with variable modalities is interesting per se, and we formulate some natural (open) questions about this logic.