How to best nest regular path queries

Regular path queries (RPQs) define query patterns in terms of regular expressions and are therefore well-suited to query for paths over roles in DL. RPQs can be extended to 2-way RPQs (with converse), CRPQs (with conjunctions), or PRPQs (arbitrary positive Boolean combinations), all of which have been explored in DL research. Another natural extension of any query language is nesting, where query predicates can be defined in terms of subqueries. In this paper, we discuss several ways of introducing nesting to PRPQs, and show that they lead to increasingly expressive query languages: CN2RPQs, which were studied in the context of DLs recently; nested P2RPQs; and positive queries with transitive closure on binary predicates. The latter is one of the most expressive languages for which query answering can still be decided over DL knowledge bases. We present initial complexity results that show query answering to be nonelementary in the worst case, with an exponential increase for each level of nesting of the transitive closure operator.