We are interested in generating new small molecules which could act as inhibitors of a biological target, when there is limited prior information on target-specific inhibitors. This form of drug-design is assuming increasing importance with the advent of new disease threats for which known chemicals only provide limited information about target inhibition. In this paper, we propose the combined use of deep neural networks and Inductive Logic Programming (ILP) that allows the use of symbolic domain-knowledge (B) to explore the large space of possible molecules. Assuming molecules and their activities to be instances of random variables X and Y , the problem is to draw instances from the conditional distribution of X, given Y, B (D X|Y,B ). We decompose this into the constituent parts of obtaining the distributions D X|B and D Y |X,B , and describe the design and implementation of models to approximate the distributions. The design consists of generators (to approximate D X|B and D X|Y,B ) and a discriminator (to approximate D Y |X,B ). We investigate our approach using the well-studied problem of inhibitors for the Janus kinase (JAK) class of proteins. We assume first that if no data on inhibitors are available for a target protein (JAK2), but a small numbers of inhibitors are known for homologous proteins (JAK1, JAK3 and TYK2). We show that the inclusion of relational domainknowledge results in a potentially more effective generator of inhibitors than simple random sampling from the space of molecules or a generator without access to symbolic relations. The results suggest a way of combining symbolic domain-knowledge and deep generative models to constrain the exploration of the chemical space of molecules, when there is limited information on target-inhibitors. We also show how samples from the conditional generator can be used to identify potentially novel target inhibitors.