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Argumentative relation classification is the task of determining the type of relation (e.g., support or attack) that holds between two argument units. Current state-of-the-art models primarily exploit surface-linguistic features including discourse markers, modals or adverbials to classify argumentative relations. However, a system that performs argument analysis using mainly rhetorical features can be easily fooled by the stylistic presentation of the argument as opposed to its content, in cases where a weak argument is concealed by strong rhetorical means. This paper explores the difficulties and the potential effectiveness of knowledge-enhanced argument analysis, with the aim of advancing the state-of-the-art in argument analysis towards a deeper, knowledge-based understanding and representation of arguments. We propose an argumentative relation classification system that employs linguistic as well as knowledge-based features, and investigate the effects of injecting background knowledge into a neural baseline model for argumentative relation classification. Starting from a Siamese neural network that classifies pairs of argument units into support vs. attack relations, we extend this system with a set of features that encode a variety of features extracted from two complementary background knowledge resources: ConceptNet and DBpedia. We evaluate our systems on three different datasets and show that the inclusion of background knowledge can improve the classification performance by considerable margins. Thus, our work offers a first step towards effective, knowledge-rich argument analysis.