Logic-based argumentation offers an approach to querying and revising multiple ontologies that are inconsistent or incoherent. A common assumption for logic-based argumentation is that an argument is a pair Φ,α where Φ is a minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claim α. Using dialogue games, agents (each with its own ontology) can exchange arguments and counterarguments concerning formulae of interest. In this paper, we present a novel framework for logic-based argumentation with ontological knowledge. As far as we know, this is the first proposal for argumentation with multiple ontologies via dialogues. It allows two agents to discuss the answer to queries concerning their knowledge (even if it is inconsistent) without one agent having to copy all of their ontology to the other, and without the other agent having to expend time and effort merging that ontology with theirs. Furthermore, it offers the potential for the agents to incrementally improve their knowledge based on the dialogue by checking how it differs from the other agent's.