Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

The International Joint Conference on Artificial Intelligence (IJCAI), 2020.

Zakharyaschev M., Kontchakov R., Ryzhikov V., Wolter F.

Traditionally, description logic has focused on represent- ing and reasoning about classes rather than relations (roles), which has been justified by the deterioration of the computa- tional properties if expressive role inclusions are added. The situation is even worse in the temporalised setting, where monodicity is viewed as an almost necessary condition for decidability. We take a fresh look at the description logic DL- Lite with expressive role inclusions, both with and without a temporal dimension. While we confirm that full Boolean expressive power on roles leads to FO2-like behaviour in the atemporal case and undecidability in the temporal case, we show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to much lower complexity in the atemporal case and to decidability (and EXPSPACE- completeness) in the temporal case, even if one admits full Booleans on concepts. The latter result is one of very few in- stances breaking the monodicity barrier in temporal FO. This is also reflected on the data complexity level, where we ob- tain new rewritability results into FO with relational primitive recursion and FO with unary divisibility predicates.

Keywords: Computational Complexity, Description logics