State of the art algorithms for many pattern recognition problems rely on data-driven deep network models. Training these models requires a large labeled dataset and considerable computational resources. Also, it is difficult to understand the working of these learned models, limiting their use in some critical applications. Toward addressing these limitations, our architecture draws inspiration from research in cognitive systems, and integrates the principles of commonsense logical reasoning, inductive learning, and deep learning. As a motivating example of a task that requires explainable reasoning and learning, we consider Visual Question Answering in which, given an image of a scene, the objective is to answer explanatory questions about objects in the scene, their relationships, or the outcome of executing actions on these objects. In this context, our architecture uses deep networks for extracting features from images and for generating answers to queries. Between these deep networks, it embeds components for non-monotonic logical reasoning with incomplete commonsense domain knowledge, and for decision tree induction. It also incrementally learns and reasons with previously unknown constraints governing the domain's states. We evaluated the architecture in the context of datasets of simulated and real-world images, and a simulated robot computing, executing, and providing explanatory descriptions of plans and experiences during plan execution. Experimental results indicate that in comparison with an “end to end” architecture of deep networks, our architecture provides better accuracy on classification problems when the training dataset is small, comparable accuracy with larger datasets, and more accurate answers to explanatory questions. Furthermore, incremental acquisition of previously unknown constraints improves the ability to answer explanatory questions, and extending non-monotonic logical reasoning to support planning and diagnostics improves the reliability and efficiency of computing and executing plans on a simulated robot.