While argument mining has achieved significant success in classifying argumentative relations between statements (support, attack, and neutral), we have a limited computational understanding of logical mechanisms that constitute those relations. Most recent studies rely on black-box models, which are not as linguistically insightful as desired. On the other hand, earlier studies use rather simple lexical features, missing logical relations between statements. To overcome these limitations, our work classifies argumentative relations based on four logical and theory-informed mechanisms between two statements, namely (i) factual consistency, (ii) sentiment coherence, (iii) causal relation, and (iv) normative relation. We demonstrate that our operationalization of these logical mechanisms classifies argumentative relations without directly training on data labeled with the relations, significantly better than several unsupervised baselines. We further demonstrate that these mechanisms also improve supervised classifiers through representation learning.