EXPLORING NON-REGULAR EXTENSIONS OF PROPOSITIONAL

We investigate the impact of non-regular path expressions on the decidability of satisfiability checking and querying in description logics extending AEC. Our primary objects of interest are AECreg and AECvpl, the extensions of AEC with path expressions employing, respectively, regular and visibly-pushdown languages. The first one, AECreg, is a notational variant of the well-known Propositional Dynamic Logic of Fischer and Ladner. The second one, AECvpl, was introduced and investigated by Lo<spacing diaeresis>ding and Serre in 2007. The logic AECvpl generalises many known decidable non-regular extensions of AECreg. We provide a series of undecidability results. First, we show that decidability of the concept satisfiability problem for AECvpl is lost upon adding the seemingly innocent Self operator. Second, we establish undecidability for the concept satisfiability problem for AECvpl extended with nominals. Interestingly, our undecidability proof relies only on one single non-regular (visibly-pushdown) language, namely on r#s# := {r n s n | n is an element of N } for fixed role names r and s . Finally, in contrast to the classical database setting, we establish undecidability of query entailment for queries involving non-regular atoms from r#s#, already in the case of AEC-TBoxes.