Abstract
Non-normal modal logics based on neighbourhood semantics can be used to formalise normative, epistemic and coalitional reasoning in autonomous and multi-agent systems, since they do not validate principles known to be problematic in applications. These principles, satisfied by all modal logics interpreted over relational frames, also affect several modal description logics (MDLs) used in knowledge representation. We study non-normal MDLs, obtained by extending ALC-based languages with non-normal modal operators. These logics increase the expressive power of their propositional counterparts, and allow for complex modelling of obligations, beliefs, abilities and strategies. On the computational side, standard reasoning tasks are not more difficult than in basic normal MDLs, with a NExpTime upper bound for satisfiability that can be lowered further in fragments with modal operators only over axioms.