Nowadays, chatbot technologies are extensively used for developing conversational agents that exhibit increasingly intelligent communicative behaviour. As relatively new technologies, chatbots give us numerous research opportunities to refine them, particularly through the neurosymbolic integration with other technologies from the emerging field of Artificial Intelligence (AI). In this paper, we explore the ability of chatbot technologies to classify arguments according to several reasoning patterns, i.e. informal arguments, called argument schemes. Since argumentation is a significant aspect of human intelligence, categorising arguments according to various argumentation schemes that reflect human reasoning patterns is crucial for developing sophisticated agent-based technologies that facilitate human-computer interaction. Additionally, we evaluate how chatbots are able to handle enthymemes, where premises or conclusions are omitted from arguments rather than explicitly stated. This will enable agents (chatbots) to engage in more sophisticated interactions, such as argumentation processes, in which humans are allowed to use implicit knowledge when communicating arguments.