Number Restrictions on Transitive Roles in Description Logics with Nominals

Víctor Gutiérrez-Basulto, Yazmin Angélica Ibáñez-García, Jean Christoph Jung

Abstract:

We study description logics (DLs) supporting number restrictions
on transitive roles. We first take a look at SOQ and
SON with binary and unary coding of numbers, and provide
algorithms for the satisfiability problem and tight complexity
bounds ranging from EXPTIME to NEXPTIME. We then
show that by allowing for counting only up to one (functionality),
inverse roles and role inclusions can be added without
losing decidability. We finally investigate DLs of the DLLite-
family, and show that, in the presence of role inclusions,
the core fragment becomes undecidable.