In this paper, we tackle learning in distributed systems and the fact that learning does not necessarily involve the participation of agents directly in the inductive process itself. Instead, many systems frequently employ multiple instances of induction separately. The paper?s main contribution is a new approach that tightly integrates processes of induction between distributed agents, based on inductive logic programming techniques, for a wider class of problem solving tasks. The approach combines inverse entailment with an epistemic approach to reasoning about knowledge, facilitating a systematic approach to the sharing of knowledge and invention of predicates only when required. We illustrate the approach for learning declarative program fragments and for a well-known path planning problem and compare results empirically to (multiple instances of) single agent-based induction over varying distributions of data. Given a chosen path planning algorithm, our algorithm enables agents to combine their local knowledge in an effective way to avoid central control while significantly reducing communication costs.