Recently, neural networks have been successfully employed to improve upon state-of-the-art performance in ad-hoc retrieval tasks via machine-learned ranking functions. While neural retrieval models grow in complexity and impact, little is understood about their correspondence with well-studied IR principles. Recent work on interpretability in machine learning has provided tools and techniques to understand neural models in general, yet there has been little progress towards explaining ranking models. We investigate whether one can explain the behavior of neural ranking models in terms of their congruence with well understood principles of document ranking by using established theories from axiomatic IR. Axiomatic analysis of information retrieval models has formalized a set of constraints on ranking decisions that reasonable retrieval models should fulfill. We operationalize this axiomatic thinking to reproduce rankings based on combinations of elementary constraints. This allows us to investigate to what extent the ranking decisions of neural rankers can be explained in terms of retrieval axioms, and which axioms apply in which situations. Our experimental study considers a comprehensive set of axioms over several representative neural rankers. While the existing axioms can already explain the particularly confident ranking decisions rather well, future work should extend the axiom set to also cover the other still "unexplainable" neural IR rank decisions.