Semantic Web knowledge representation standards such as RDF and OWL have gained momentum in the last years and are widely applied today. In the course of the standardization process of these and other knowledge representation formalisms, decidability of logical entailment has often been advocated as a central design criterion. On the other hand, restricting to decidable formalisms inevitably comes with constraints in terms of modeling power. Therefore, in this paper, we examine the requirement of decidability and weigh its importance in different scenarios. Subsequently, we discuss a way to establish incomplete – yet useful – reasoning support for undecidable formalisms by deploying machinery from the successful domain of theorem proving in first-order predicate logic. While elaborating on the undecidable variants of the ontology language OWL 2 as our primary examples, we argue that this approach could likewise serve as a role model for knowledge representation formalisms from the Conceptual Structures community.