When considering two concepts in terms of extensional logic, their combination will often be trivial, returning an empty extension. Consider e.g. “a Fish Vehicle”, i.e., “a Vehicle which is also a Fish”. Still, people use sophisticated strategies to produce new, non-empty concepts. All these strategies involve the human ability to mend the conflicting attributes of the input concepts and to create new properties of the combination. We focus in particular on the case where a Head concept has superior ‘asymmetric’ control over steering the resulting combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical model of the cognitive and logical mechanics of this asymmetric form of hybridisation. Its implementation is then evaluated using a combination of example ontologies.