  We introduce Deep Adaptive Semantic Logic (DASL), a novel framework for
automating the generation of deep neural networks that incorporates
user-provided formal knowledge to improve learning from data. We provide formal
semantics that demonstrate that our knowledge representation captures all of
first order logic and that finite sampling from infinite domains converges to
correct truth values. DASL's representation improves on prior neural-symbolic
work by avoiding vanishing gradients, allowing deeper logical structure, and
enabling richer interactions between the knowledge and learning components. We
illustrate DASL through a toy problem in which we add structure to an image
classification problem and demonstrate that knowledge of that structure reduces
data requirements by a factor of $1000$. We then evaluate DASL on a visual
relationship detection task and demonstrate that the addition of commonsense
knowledge improves performance by $10.7\%$ in a data scarce setting.
