Extending ALCQIO with reachability

We introduce an extension ALCQIOb,Re of the description logic ALCQIO, a sub-logic of the two-variable fragment of first order logic with counting quantifiers, with reachability assertions. ALCQIOb,Reformulae can define an unbounded number of trees. We show that finite implication of ALCQIOb,Re-formulae is polynomial-time reducible to finite satisfiability of ALCQIO-formulae. As a consequence, we get that finite satisfiability and finite implication in ALCQIOb,Re are NEXPTIMEcomplete. Description logics with transitive closure constructors have been studied before, but ALCQIOb,Re is the first decidable description logic which allows at the same time nominals, inverse roles, counting quantifiers and transitive closures. ALCQIOb,Re is well-suited for applications in software verification and shape analysis. Shape analysis requires expressive logics with reachability which have good computational properties. We show that ALCQIOb,Re can describe complex data structures with a high degree of sharing and allows compositions such as list of trees.