Barbara Morawska

Michał Henne, Barbara Morawska, Paweł Parys

Description logics (DL) are a family of formal languages for representing and reasoning about structured knowledge in terms of concepts and their relationships. A central reasoning problem in DL is concept subsumption. Although this problem has been widely studied, important open problems remain for certain logics. The expressive power of DLs depends on the constructors available for building complex concepts. In this work, we investigate subsumption in the restricted logic $\mathcal{FL}_{\bot \mathit{reg}}$ and its related fragments $\mathcal{FL}_\mathit{reg}$, $\mathcal{FL}_\bot$, and $\mathcal{FL}_0$. These logics support value restrictions over role names, where the subscript $\bot$ denotes the presence of the empty concept and ${reg}$ denotes the use of regular expressions over roles. None of these logics includes concept negation. We show that deciding subsumption between two concept descriptions in $\mathcal{FL}_{\bot \mathit{reg}}$ and $\mathcal{FL}_\mathit{reg}$ is PSpace-complete. When subsumption is considered with respect to a TBox (i.e., a set of axioms), the complexity increases to ExpTime-complete. Our results are obtained via a novel reduction to parity pushdown games.

Franz Baader, Stefan Borgwardt, Barbara Morawska

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic $\mathcal{EL}$ to disunification since negative constraints can be used to avoid unwanted unifiers. While decidability of the solvability of general $\mathcal{EL}$-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we consider only solutions that are constructed from terms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of disunification problems.